Recent zbMATH articles in MSC 86https://zbmath.org/atom/cc/862023-11-13T18:48:18.785376ZUnknown authorWerkzeugIntroductionhttps://zbmath.org/1521.000272023-11-13T18:48:18.785376ZFrom the text: This Special Issue originates from a Special Session on ``Magnetohydrodynamics: Mathematical Problems and Astrophysical Applications'' that was held in the framework of the ``8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications'' at Dresden University of Technology from 25 to 28 May 2010. The Special Issue papers are elaborated and updated versions of several of the review talks.Optimal control of lake eutrophicationhttps://zbmath.org/1521.351732023-11-13T18:48:18.785376Z"Choquet, Catherine"https://zbmath.org/authors/?q=ai:choquet.catherine"Comte, Eloïse"https://zbmath.org/authors/?q=ai:comte.eloiseThe authors consider a domain \(\Omega \) in \(\mathbb{R}^{3}\), which represents a lake, with a \(C^{1}\) boundary \(\partial \Omega \) which is the union of three disjoint sets \(\partial \Omega =\Gamma _{\mathrm{in}}\cup \Gamma _{\mathrm{out}}\cup \Gamma \), where \(\Gamma _{\mathrm{in}}\) is the lake entrance and \(\Gamma _{\mathrm{out}}\) is the lake exit (\(\Gamma _{\mathrm{in}}\) and \(\Gamma _{\mathrm{out}}\) being not necessarily connected). They consider the space-time dynamics of the phosphorus stock \(\overline{S}\) and of the cyanobacteria concentration \(c\) in the lake written in \(\Omega \times (0,T)\) as: \(\partial _{t}\overline{S} +\operatorname{div}(v\overline{S})-d_{s}\Delta \overline{S}+b(\overline{S})\overline{S}-h( \overline{S})+f(\overline{S},c)c=0\), \(\partial _{t}c+\operatorname{div}(vc)-d_{c}\Delta c+m(c)c-f(\overline{S},c)c=0\), where \(v\) is the velocity which governs the convection, \(d_{s}\) and \(d_{c}\) diffusion coefficients, \(b\) and \(m\) nonlinear functions which represent the rates of loss per unit stock and per cyanobacteria concentration, \(h(\overline{S})=\overline{S}^{2}/(k+\overline{S }^{2})\) models the internal discharge of the phosphorus trapped in the sediments, and \(f\) the Monod term, often chosen in the form \(f(\overline{S} )=u_{max}\overline{S}/(k_{s}+\overline{S})\), which relates the phosphorus stock with the cyanobacterial dynamics, \(u_{\max}\) representing the maximal increasing rate and \(k_{s}\) the half-saturation value.
The initial conditions \(\overline{S}\mid _{t=0}=\overline{S}_{0}\), \(c\mid _{t=0}=c_{0}\) are imposed in \(\Omega \), together with the boundary conditions: \((\overline{ S}v-d_{s}\nabla \overline{S})\cdot n=(cv-d_{c}\nabla c)\cdot n=0\), on \( (0,T)\times \Gamma \), \(r_{S}\overline{S}+(\overline{S}v-d_{s}\nabla \overline{S})\cdot n=R_{S}(\overline{S})\), with \(r_{S}\leq 0\), \( r_{c}c+(cv-d_{c}\nabla c)\cdot n=R_{c}(c)\), with \(r_{c}\leq 0\), on \( (0,T)\times \Gamma _{\mathrm{out}}\), \(\overline{S}=\overline{P}\), \((cv-d_{c}\nabla c)\cdot n=0\), on \((0,T)\times \Gamma _{\mathrm{in}}\). Assuming further hypotheses on the different terms of the parabolic problem, the authors prove the existence of a unique weak solution \((\overline{S},c)\in (L^{2}(0,T;H^{1}(\Omega ))\cap L^{\infty }(0,T;L^{2}(\Omega ))^{2}\) to this problem.
For the proof, the authors propose a variational formulation of the above parabolic problem and they use the Faedo-Galerkin method, maximum principles and a uniqueness result. They then propose an optimal control associated to the above problem written as: Find \((\overline{P}^{\ast }, \overline{S}^{\ast },c^{\ast })\) such that \(J(\overline{P}^{\ast },c^{\ast })=\max\{J(\overline{P},c)\); \(\overline{P}\in E\) with \((\overline{S},c)\) satisfying the above parabolic problem\(\}\). Here \(E\) is the set of admissible controls defined as \(E=\{\overline{P}\in L^{\infty }((0,T)\times \Gamma _{in})\); \(0\leq \overline{P}(t,x)\leq \overline{P}_{\max}\) a.e. in \( (0,T)\times \Gamma _{in}\}\), where \(\overline{P}_{\max}\) is any given real number, and \(J\) the objective function defined as: \(J(\overline{P} ,c)=\int_{0}^{T}\left( \int_{\Gamma _{\mathrm{in}}}B(t,\sigma ,\overline{P}(t,\sigma ))e^{-\rho t}d\sigma -\int_{\Omega }D(t,x,c(t,x))e^{-\rho t}dx\right) dt\), where \(\rho \in ]0,1[\) is the social discount rate and \((\overline{S},c)\) satisfies the above parabolic problem. Setting \(S=\overline{S}-P\), where \(P\) is the unique solution to: \(\partial _{t}P-d_{s}\Delta P=0\) in \(\Omega \times (0,T)\), \(P\mid _{t=0}=P_{0}\) in \(\Omega \), \(P\mid _{\Gamma _{in}}= \overline{P}\), \(P\mid _{\partial \Omega \setminus \Gamma _{\mathrm{in}}}=0\) on \( \partial \Omega \times (0,T)\), \(P_{0}\) being the solution to: \(-\Delta P_{0}=0\) in \(\Omega \), \(P\mid _{\Gamma _{in}}=\overline{P}\mid _{t=0}\), \( P_{0}\mid _{\partial \Omega \setminus \Gamma _{in}}=0\) on \(\partial \Omega \times (0,T)\), the authors rewrite the above problem and the optimal control problem. Under the same hypotheses as in the existence and uniqueness result for a weak solution to the parabolic problem, they prove the existence of a global solution \((\overline{P}^{\ast },\overline{S}^{\ast },c^{\ast })\) to the optimal control problem. The proof is based on some boundedness property of a maximizing sequence for the objective function \(J\) and on the analysis of the convergence of this sequence.
Reviewer: Alain Brillard (Riedisheim)Bäcklund transformation, infinite number of conservation laws and fission properties of an integro-differential model for ocean internal solitary waveshttps://zbmath.org/1521.370822023-11-13T18:48:18.785376Z"Yu, Di"https://zbmath.org/authors/?q=ai:yu.di"Zhang, Zong-Guo"https://zbmath.org/authors/?q=ai:zhang.zongguo"Dong, Huan-He"https://zbmath.org/authors/?q=ai:dong.huanhe"Yang, Hong-Wei"https://zbmath.org/authors/?q=ai:yang.hongweiSummary: This paper presents an analytical investigation of the propagation of internal solitary waves in the ocean of finite depth. Using the multi-scale analysis and reduced perturbation methods, the integro-differential equation is derived, which is called the intermediate long wave (ILW) equation and can describe the amplitude of internal solitary waves. It can reduce to the Benjamin-Ono equation in the deep-water limit, and to the KdV equation in the shallow-water limit. Little attention has been paid to the features of integro-differential equations, especially for their conservation laws. Here, based on Hirota bilinear method, Bäcklund transformations in bilinear form of ILW equation are derived and infinite number of conservation laws are given. Finally, we analyze the fission phenomenon of internal solitary waves theoretically and verify it through numerical simulation. All of these have potential value for the further research on ocean internal solitary waves.On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciologyhttps://zbmath.org/1521.651242023-11-13T18:48:18.785376Z"de Diego, Gonzalo G."https://zbmath.org/authors/?q=ai:g-de-diego.gonzalo"Farrell, Patrick E."https://zbmath.org/authors/?q=ai:farrell.patrick-e|farrell.patrick-emmet"Hewitt, Ian J."https://zbmath.org/authors/?q=ai:hewitt.ian-jIn this work, the problem of a marine ice sheet resting on a bedrock and sliding into the ocean, where it goes afloat is considered. The suitable contact conditions transform the instantaneous Stokes problem into a variational inequality. The article is outlined as follows. Section 1 is an Introduction. In Section 2, the Stokes variational inequality and its mixed formulation are presented. A Korn-type inequality is proved and is demonstrated that the mixed formulation is well-posed. In Section 3, a family of finite element approximations of the mixed problem is analyzed and error estimates in terms of best approximation results for the velocity, pressure, and Lagrange multiplier are presented. In Section 4, a concrete finite element scheme involving quadratic elements for the velocity and piecewise-constant elements for the pressure and the Lagrange multiplier is introduced. Then error estimates for this scheme are presented and a problem with a manufactured solution to calculate convergence rates and compare these with the authors' estimates is solved. Numerical results are reported to validate the error estimates. Some conclusions are given in Section 5. Finally, Appendices A, B, B.1, B.2, and B.3 with fixing equivalence of formulations and technical results on finite element spaces are given.
Reviewer: Temur A. Jangveladze (Tbilisi)An improved grain-based numerical manifold method to simulate deformation, damage and fracturing of rocks at the grain size levelhttps://zbmath.org/1521.740372023-11-13T18:48:18.785376Z"Zhou, Guang-lei"https://zbmath.org/authors/?q=ai:zhou.guanglei"Xu, Tao"https://zbmath.org/authors/?q=ai:xu.tao"Konietzky, Heinz"https://zbmath.org/authors/?q=ai:konietzky.heinz"Zhu, Wancheng"https://zbmath.org/authors/?q=ai:zhu.wancheng"Heng, Zhen"https://zbmath.org/authors/?q=ai:heng.zhen"Yu, Xian-yang"https://zbmath.org/authors/?q=ai:yu.xianyang"Zhao, Yong"https://zbmath.org/authors/?q=ai:zhao.yong.2Summary: An improved grain-based numerical manifold method (NMM) is developed to investigate deformation and damage of intact rocks at the meso-scale. The grain boundaries are embedded into the numerical manifold method using a random Voronoi tessellation technique to approximate the microstructure of rocks at the meso-scale. To enhance efficiency, an improved contact loop updating algorithm is proposed, which only preserves the corners of polygonal blocks and deletes the rest of the loop boundary nodes, thus greatly reducing the number of loop nodes involved in contact retrieval. An interface contact model considering cohesion and tensile strength between rock grains is incorporated into the numerical manifold method to simulate fracturing. With the newly developed grain-based numerical manifold method, Brazilian tests and uniaxial compression tests are numerically simulated to validate failure pattern and macroscopic response against laboratory tests. Sensitivity analysis is conducted using the proposed model to further investigate the influence of different number of grains and different stiffness ratio on the macroscopic response of rocks. The results indicate that the improved grain-based numerical manifold method can be effectively used to study deformation, damage and fracturing of rocks at the meso-scale.Three-dimensional preconditioned FM-IBEM solution to broadband-frequency seismic wave scattering in a layered sedimentary basinhttps://zbmath.org/1521.741182023-11-13T18:48:18.785376Z"Liu, Zhong-Xian"https://zbmath.org/authors/?q=ai:liu.zhongxian"Huang, Zhen-En"https://zbmath.org/authors/?q=ai:huang.zhen-en"Zhang, Zheng"https://zbmath.org/authors/?q=ai:zhang.zheng.8"Meng, Si-Bo"https://zbmath.org/authors/?q=ai:meng.si-bo"Huang, Lei"https://zbmath.org/authors/?q=ai:huang.leiSummary: A three-dimensional (3-D) fast multipole indirect boundary element method (FM-IBEM) combined with an inner-outer preconditioned generalized minimal residual (GMRES) method algorithm is proposed to solve the broadband-frequency seismic wave scattering problem in complex sites. This method is established in three steps: first, the scattering wave field is developed with the dynamic Green's function; second, the dynamic Green's functions are expanded to generate a traditional FM-IBEM framework; and finally, the preconditioning matrix and GMRES algorithm are introduced to pre-process the dynamic Green's functions. Using this method, the broadband-frequency scattering of normally incident seismic waves in a hemispherical layered sedimentary basin is investigated in the frequency and time domains. The results show that the proposed method is highly accurate and efficient for solving low- and high-frequency seismic wave problems. Compared with the FM-IBEM without preconditioning, the computational time and storage space required for the FM-IBEM with preconditioning are reduced by 84\% and 54\%, respectively. The layered sedimentary basin has significant wave amplification (of up to 10 times) for dimensionless frequencies, \(\eta\), in the range of 0.5--3.0; however, for \(\eta>5\), the amplification effect becomes weak.Pounding mitigation of a short-span cable-stayed bridge using a new hybrid passive control systemhttps://zbmath.org/1521.741212023-11-13T18:48:18.785376Z"Javanmardi, Ahad"https://zbmath.org/authors/?q=ai:javanmardi.ahad"Ghaedi, Khaled"https://zbmath.org/authors/?q=ai:ghaedi.khaled"Ibrahim, Zainah"https://zbmath.org/authors/?q=ai:ibrahim.zainah"Huang, Fuyun"https://zbmath.org/authors/?q=ai:huang.fuyun"Kuczma, Mieczysław"https://zbmath.org/authors/?q=ai:kuczma.mieczyslaw-s"Tabrizikahou, Alireza"https://zbmath.org/authors/?q=ai:tabrizikahou.alireza"Mohammad-Sedighi, Hamid"https://zbmath.org/authors/?q=ai:sedighi.hamid-mohammadSummary: This paper investigates the effectiveness of a new hybrid passive control system on the seismic response of an existing steel cable-stayed bridge considering the pounding effect. The proposed hybrid passive control system comprises a seismic isolator and a metallic damper. The bridge is located in a high seismic zone and has suffered several damages including the earthquake-induced pounding damage during the 1988 earthquake. Thereby, the proposed hybrid passive control system was investigated for seismic retrofitting of the bridge to mitigate the seismic damages due to future earthquakes. The hybrid control system was placed at the bridge ends and the tower-deck connection. A detailed three-dimensional finite element model of the bridge was created and validated with the earlier experimental results. A comparative analysis was performed through a series of nonlinear dynamic time-history analyses on the bridge equipped with the proposed and other control systems. The results showed that the hybrid control system reduced the bridge's longitudinal seismic displacement, mitigated the pounding of the bridge with abutments and improved the overall seismic performance of the bridge.Action of an oblique seismic wave on an underground pipelinehttps://zbmath.org/1521.741512023-11-13T18:48:18.785376Z"Israilov, M. Sh."https://zbmath.org/authors/?q=ai:israilov.m-sh(no abstract)Wave effect of front topography based on modified time-frequency transform methodhttps://zbmath.org/1521.741542023-11-13T18:48:18.785376Z"Li, Minghe"https://zbmath.org/authors/?q=ai:li.minghe"Yang, Zailin"https://zbmath.org/authors/?q=ai:yang.zailin"Yang, Yong"https://zbmath.org/authors/?q=ai:yang.yong.1Summary: In this paper, a modified time-frequency transform method is proposed by introducing a modified factor based on elastic wave theory and classical Fourier transform. The feasibility of the proposed method is verified by taking the front semi-cylindrical canyon and hill topography subject to horizontal anti-plane shear waves as the research object. Based on the analytical solution of wave field in frequency domain and modified time-frequency transform method, the modified wave field in time domain and the amplitude of surface displacement are obtained, and the wave effect of the front terrain is discussed. The results show that the wave effect of front canyon is stronger than that of the hill, and the range is wider that cannot be ignored under thousands of characteristic radii. The results and the proposed modified time-frequency transform method can provide theoretical reference and a new idea for earthquake engineering.Time effect of vertically loaded pile groups partially embedded in multilayered cross-anisotropic fractional viscoelastic saturated soilshttps://zbmath.org/1521.741552023-11-13T18:48:18.785376Z"Lu, Qing Song"https://zbmath.org/authors/?q=ai:lu.qing-song"Ai, Zhi Yong"https://zbmath.org/authors/?q=ai:ai.zhiyong"Jiang, Ming Jing"https://zbmath.org/authors/?q=ai:jiang.mingjing"Liu, Wen Jie"https://zbmath.org/authors/?q=ai:liu.wen-jieSummary: This paper investigates the time-varying mechanical performance of partially embedded pile groups subjected to vertical loads in multilayered cross-anisotropic fractional viscoelastic saturated soils. Piles are considered as one-dimensional compression bars and the stiffness matrix of a single pile and the global stiffness matrix of partially embedded pile groups are obtained by the finite element method. Based on the boundary element method, the soil stiffness matrix is deduced by expanding the extended precise integration solution. Then, the solution for partially embedded pile groups in multilayered fractional viscoelastic saturated soils is derived by employing the boundary element-finite element coupling method. Comparisons with existing solutions and an ABAQUS model prove the correctness of the proposed method. Numerical analyses are carried out to evaluate the influences of fractional derivative order, free length, pile spacing, pile-soil stiffness ratio as well as soil stratification on the time effect of partially embedded pile groups under vertical loads.The virtual element method for rock mass with frictional crackshttps://zbmath.org/1521.741572023-11-13T18:48:18.785376Z"Sun, Yinghao"https://zbmath.org/authors/?q=ai:sun.yinghao"Yi, Qi"https://zbmath.org/authors/?q=ai:yi.qi"Wang, Jiao"https://zbmath.org/authors/?q=ai:wang.jiao"Sun, Guanhua"https://zbmath.org/authors/?q=ai:sun.guanhuaSummary: This paper presents the frictional contact formulation for frictional crack in elastic solids at small strains based on the Penalty method in the framework of the virtual element method. For normal direction of contact interface, the Karush-Kuhn-Tucker conditions (or KKT-conditions) is engaged to handle the contact problem. The Coulomb's law is exerted to respond to the crack interface's stick-slip condition for the tangential direction of the contact interface. The frictional contact constraints are forced by the classical Penalty method and the node-to-segment approach is applicated to compute the contact element on the contact interface. Several numerical examples with Voronoi meshes are offered to display the contact algorithm accuracy compared with existing results in the imitation of a variety of contact conditions. In the last numerical simulations, the contact algorithm is also suitable for the rock mass with multiple cracks.Fracturing failure simulations of rock discs with pre-existing cracks by numerical manifold methodhttps://zbmath.org/1521.741942023-11-13T18:48:18.785376Z"Ning, Youjun"https://zbmath.org/authors/?q=ai:ning.youjun"Lu, Qi"https://zbmath.org/authors/?q=ai:lu.qi|lu.qi.1|lu.qi.2"Liu, Xinlian"https://zbmath.org/authors/?q=ai:liu.xinlian(no abstract)Coupled FEM/SBFEM investigation on the characteristic analysis of seismic motions of a trapezoidal canyon in a layered half-spacehttps://zbmath.org/1521.742662023-11-13T18:48:18.785376Z"Yanpeng, Li"https://zbmath.org/authors/?q=ai:yanpeng.li"Zhiyuan, Li"https://zbmath.org/authors/?q=ai:zhiyuan.li"Zhiqiang, Hu"https://zbmath.org/authors/?q=ai:zhiqiang.hu"Gao, Lin"https://zbmath.org/authors/?q=ai:gao.linSummary: Layered topographies and geologies are known to have considerable effects on the spatially variable seismic motions scattered by a canyon in a layered half-space. In this study, based on a substructure replacement technique, a coupled finite element method and scaled boundary finite element method based on scaling splicing lines (hereafter referred to as coupled FEM/SBFEM) is developed for a scattering field analysis, considering the effect of the layered topographical characteristics. The near field is modelled using the finite element method (FEM), and the far field is modelled using an improved scaled boundary finite element method, which can model the radiation damping of a layered half-space precisely. In the modified version of SBFEM, a novel dimensionless frequency is proposed to facilitate obtaining the time-domain response efficiently using a fast Fourier transformation. Several examples are investigated to demonstrate the versatility and validity of the proposed method. Parametric studies are performed to investigate the characteristics of the ground motions of a trapezoidal canyon in a layered half-space in the frequency and time domains (where the ground motions significantly differ from those of a uniform half-space), and to investigate the effects on ground motions caused by the soil layer thickness, burial depth, and impedance ratio.Dynamic analysis of anti-dip bedding rock slopes reinforced by pre-stressed cables using discrete element methodhttps://zbmath.org/1521.742782023-11-13T18:48:18.785376Z"Zheng, Yun"https://zbmath.org/authors/?q=ai:zheng.yun"Wang, Runqing"https://zbmath.org/authors/?q=ai:wang.runqing"Chen, Congxin"https://zbmath.org/authors/?q=ai:chen.congxin"Sun, Chaoyi"https://zbmath.org/authors/?q=ai:sun.chaoyi"Ren, Zhanghao"https://zbmath.org/authors/?q=ai:ren.zhanghao"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.240Summary: Pre-stressed cables were found to be a viable approach of reinforcing anti-dip bedding rock slopes (ABRSs) in the Wenchuan earthquake. However, the dynamic response law and failure mechanism of reinforced ABRSs are still unclear, which was studied using the Universal Distinct Element Code (UDEC) method in this work. A numerical model of a typical ABRS was first built up using UDEC. Then, a comparison of the dynamic response of reinforced and unreinforced ABRSs was carried out. Moreover, a systematic parameter study was performed to investigate the effect of cable inclination, cable spacing, and pre-stressed force on the reinforcement effect. The results show that pre-stressed cables can be very effective in controlling the deformation and improving the dynamic stability of ABRSs subjected to dynamic loading. For both unreinforced and reinforced ABRSs, a remarkable acceleration amplification occurs on the surface of the slope from half of the slope height upwards. A small cable inclination and a high pre-stressed force are recommended in the seismic reinforcement design of ABRSs. The results of this work could guide the design of reinforcement of ABRS in earthquake-prone areas.Elastic wave field simulation of a three-dimensional sedimentary basin for incident spherical P, SV, and SH waveshttps://zbmath.org/1521.742922023-11-13T18:48:18.785376Z"Ba, Zhenning"https://zbmath.org/authors/?q=ai:ba.zhenning"Fu, Jisai"https://zbmath.org/authors/?q=ai:fu.jisai"Liu, Yue"https://zbmath.org/authors/?q=ai:liu.yue.3"Wang, Ying"https://zbmath.org/authors/?q=ai:wang.ying.37Summary: In this paper, the source is assumed to be a more realistic spherical wave than plane wave, and the scattering of spherical P, SV and SH waves by 3D sedimentary basins is studied by using IBEM. The total wave field is decomposed into free wave field and scattered wave field. The free wave field is solved by direct stiffness method combined with Hankel transformation, while the scattered wave field is simulated by dynamic Green's function. The correctness of the method is verified by comparing the results calculated by this method with those in published literature. Taking the model of a semi elliptical sedimentary basin as an example, the effects of source location, incident wave frequency, shear wave velocity ratio between bedrock and single rock on surface displacement amplitude are studied. The results show that: under the incident of spherical wave source, the sedimentary basin has obvious amplification effect on the surface displacement for different source location, and the larger the incident frequency, more obvious the amplification effect is; in the layered half-space, when the incident frequency is low, the shear wave velocity ratio has a significant effect on the basin surface displacement.Effects of adjacent paleochannel sedimentary on the seismic response of structure with incident SH-wavehttps://zbmath.org/1521.742932023-11-13T18:48:18.785376Z"Ba, Zhenning"https://zbmath.org/authors/?q=ai:ba.zhenning"Fu, Jisai"https://zbmath.org/authors/?q=ai:fu.jisai"Wang, Fangbo"https://zbmath.org/authors/?q=ai:wang.fangbo"Yao, Xiaowen"https://zbmath.org/authors/?q=ai:yao.xiaowen(no abstract)A three-dimensional indirect boundary integral equation method for the scattering of seismic waves in a poroelastic layered half-spacehttps://zbmath.org/1521.743232023-11-13T18:48:18.785376Z"Huang, Lei"https://zbmath.org/authors/?q=ai:huang.lei"Liu, Zhongxian"https://zbmath.org/authors/?q=ai:liu.zhongxian"Wu, Chengqing"https://zbmath.org/authors/?q=ai:wu.chengqing"Liang, Jianwen"https://zbmath.org/authors/?q=ai:liang.jianwen"Pei, Qiang"https://zbmath.org/authors/?q=ai:pei.qiang(no abstract)A special indirect boundary element method for seismic response of a 3D canyon in a saturated layered half-space subjected to obliquely incident plane waveshttps://zbmath.org/1521.743322023-11-13T18:48:18.785376Z"Liang, Jianwen"https://zbmath.org/authors/?q=ai:liang.jianwen"Wang, Yongguang"https://zbmath.org/authors/?q=ai:wang.yongguang"Ba, Zhenning"https://zbmath.org/authors/?q=ai:ba.zhenning"Zhong, Hao"https://zbmath.org/authors/?q=ai:zhong.haoSummary: A special indirect boundary element method (IBEM) is proposed to deal with the wave scattering of plane P1-, SV- and SH-waves by a 3D canyon cut in a saturated layered half-space. First, the dynamic stiffness matrix method is used to determine the free field dynamic responses. Then, based on Biot's theory, the 3D dynamic Green's functions for uniformly distributed loads and pore pressure acting on an inclined plane in a saturated layered half-space are derived, which is subsequently utilized to construct the scattered fields. Finally, the densities of uniformly distributed loads are determined by introducing boundary conditions, and the total dynamic responses are obtained by superimposing the free and scattered fields. The accuracy of the proposed method is verified via the comparison between the calculated results and those of published literature. The influences of boundary drainage conditions, medium porosity, and soil layering on seismic response are investigated in the frequency domain through parametric analysis. The numerical results show that the influences of boundary drained conditions on dynamic response are apparent, especially for high incident frequency. The effect of porosity on dynamic response seems to more sensitive to undrained conditions. Furthermore, the soil layering will bring an impact on the scattering mechanism of the layered system, appearing difference in the displacement amplitude and its distribution.Indirect boundary element method solution to the seismic ground motion of near-fault sedimentary valleyhttps://zbmath.org/1521.743372023-11-13T18:48:18.785376Z"Liu, Zhongxian"https://zbmath.org/authors/?q=ai:liu.zhongxian"Liu, Ying"https://zbmath.org/authors/?q=ai:liu.ying.23|liu.ying"Huang, Lei"https://zbmath.org/authors/?q=ai:huang.lei"Li, Yurun"https://zbmath.org/authors/?q=ai:li.yurun"Zhao, Ruibin"https://zbmath.org/authors/?q=ai:zhao.ruibinSummary: In this paper, the indirect boundary element method (IBEM) is developed to solve the ground motion effect of the near-fault complex site. By establishing a two-dimensional kinematic finite fault model, the amplification effect of seismic response of sedimentary valley under the continuous dislocation of reverse faults is quantitatively analyzed. Meanwhile, the influence of the parameters such as the buried depth of the fault top, the fault dip-angle, the fault distance of sedimentary valley, the fault-plane shape, and the rupture velocity of fault on the seismic response are studied. The results show that the sedimentary valley has a pronounced amplification effect on the seismic response induced by near-fault, and the peak value of the acceleration response spectrum of the analyzed model can be amplified by 99.3\%. In the sedimentary valley, the duration of earthquake motion is significantly prolonged, and the long-period velocity pulse appears, and the first velocity pulse can be amplified by 68.7\%. The near-fault ground motion damages have typical concentration-effect and hanging wall effect. This study provides a new and effective method, which is of great significance for seismic zoning of complex sites near-fault. It will be of guiding significance for regional planning and seismic fortification of near-fault sites.Axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressurehttps://zbmath.org/1521.743682023-11-13T18:48:18.785376Z"Xiao, Sha"https://zbmath.org/authors/?q=ai:xiao.sha"Yue, Zhongqi Quentin"https://zbmath.org/authors/?q=ai:yue.zhongqi-quentinSummary: This paper presents an axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure. The problem is of interest to understand the behavior of volcanoes, tectonic earthquakes and other oil and gas reservoirs. The volcano-shaped mantle ground topography and the internal spherical or ellipsoidal cavity are added to the conventional model of layered halfspace. The analysis uses the axisymmetric boundary element method (BEM) associated with the fundamental solution of a multilayered elastic fullspace subject to the concentrated ring-body force. The BEM is further verified for its high efficiency and accuracy by comparing its result with the analytical and FEM solutions for the problem of a homogeneous elastic halfspace whose spherical cavity is under internal pressure. The BEM is used to examine the effect of the volcano-shaped mantle, the cavity shape, the layered material properties and the internal pressure on the elastic behavior of the halfspace under the internal pressure loading within the cavity. The displacements and stresses at the external and internal boundaries and within the layered halfspace are presented and analyzed in detail. The presence of the volcano-shaped mantle can reduce significantly the swelling ground movement induced by the expansive pressure in the cavity in the layered halfspace. The cavity shape can have significant effect to the location and magnitude of the maximum tensile principal hoop stress on the cavity surface induced by its internal pressure.Performance analysis of Volna-OP2 -- massively parallel code for tsunami modellinghttps://zbmath.org/1521.760042023-11-13T18:48:18.785376Z"Giles, Daniel"https://zbmath.org/authors/?q=ai:giles.daniel"Kashdan, Eugene"https://zbmath.org/authors/?q=ai:kashdan.eugene"Salmanidou, Dimitra M."https://zbmath.org/authors/?q=ai:salmanidou.dimitra-m"Guillas, Serge"https://zbmath.org/authors/?q=ai:guillas.serge"Dias, Frédéric"https://zbmath.org/authors/?q=ai:dias.fredericSummary: The software package Volna-OP2 is a robust and efficient code capable of simulating the complete life cycle of a tsunami whilst harnessing the latest High Performance Computing (HPC) architectures. In this paper, a comprehensive error analysis and scalability study of the GPU version of the code is presented. A novel decomposition of the numerical errors into the dispersion and dissipation components is explored. Most tsunami codes exhibit amplitude smearing and/or phase lagging/leading, so the decomposition shown here is a new approach and novel tool for explaining these occurrences.
To date, Volna-OP2 has been widely used by the tsunami modelling community. In particular its computational efficiency has allowed various sensitivity analyses and uncertainty quantification studies. Due to the number of simulations required, there is always a trade-off between accuracy and runtime when carrying out these statistical studies. The analysis presented in this paper will guide the user towards an acceptable level of accuracy within a given runtime.Effect of the viscoelasticity of an ice cover on wave resistance and lift force experienced by Joubert submarinehttps://zbmath.org/1521.760522023-11-13T18:48:18.785376Z"Pogorelova, Alexandra V."https://zbmath.org/authors/?q=ai:pogorelova.alexandra-v"Zemlyak, Vitali L."https://zbmath.org/authors/?q=ai:zemlyak.vitali-l"Kozin, Victor M."https://zbmath.org/authors/?q=ai:kozin.victor-mSummary: The article touches upon an unsteady rectilinear motion of a submarine in a liquid under an ice cover. The ice cover is modeled as a viscoelastic plate. The viscoelastic properties of the ice are described using the Kelvin-Voigt model. The fluid is assumed to be inviscid and incompressible, and its motion is potential. Free surface fluid flow past system of one source and several sinks is used to simulate the motion of Joubert submarine. The solution of this problem is constructed analytically using the Fourier and Laplace transforms. Numerical results for the wave resistance and lift force acting on Joubert submarine are presented for different ice thicknesses, length-to-diameter ratio of a submarine, and the speed of the uniform motion. It is demonstrated that the use of a viscoelastic model for an ice cover results in a significant decrease in the maximum values of wave resistance and lift coefficients compared to the scenario of using an elastic plate model. The results indicate that when a submarine moves at realistic speeds (\(Fr < 0.7\)) under a thick ice cover (thicker than a meter), the wave resistance is less than for the same submarine moving under a free surface. The lift force for moving at these speeds under a thick ice cover is directed upwards.Analytical study of wave diffraction by an irregular surface located on a flexible base in an ice-covered fluidhttps://zbmath.org/1521.760602023-11-13T18:48:18.785376Z"Khuntia, Sagarika"https://zbmath.org/authors/?q=ai:khuntia.sagarika"Mohapatra, Smrutiranjan"https://zbmath.org/authors/?q=ai:mohapatra.smrutiranjan"Bora, Swaroop Nandan"https://zbmath.org/authors/?q=ai:bora.swaroop-nandanSummary: The reflection and transmission of surface waves propagating over an irregular surface located on a flexible base in an ice-covered fluid are analyzed within the context of linearized water wave theory. The ice-floe and flexible bed surface are assumed as narrow elastic sheets with different compositions. Under such circumstances, there are two types of proliferating waves that exist for any specific frequency. The proliferating waves having smaller wavenumber spread at just beneath the ice-floe (ice cover mode) and the other spreads over the flexible bottom of the fluid (flexural base mode). An elementary perturbation theory is used for reforming the governing boundary value problem (bvp) to a first-order bvp which is solved by utilizing the Green's function technique. The first-order correction of the reflection and transmission coefficients are calculated in the form of integrals comprising of a function which represents the base deformation. A particular example of base deformation is taken to evaluate all these coefficients and the results are depicted graphically. The major strength of the recent study is that the results for the values of reflection and transmission coefficients for both the wavenumbers are established to meet the energy relation almost exactly.The interaction of a mode-1 internal solitary wave with a step and the generation of mode-2 waveshttps://zbmath.org/1521.760662023-11-13T18:48:18.785376Z"Liu, Zihua"https://zbmath.org/authors/?q=ai:liu.zihua"Grimshaw, Roger"https://zbmath.org/authors/?q=ai:grimshaw.roger-h-j"Johnson, Edward"https://zbmath.org/authors/?q=ai:johnson.edward-rSummary: In this study, we examine the transformation of a mode-1 internal solitary wave incident on a bottom step, and the consequent generation of mode-2 internal solitary waves. A linear long-wave theory of mode coupling in the vicinity of the step is used to estimate the mode-1 and mode-2 wave reflection and transmission coefficients, and hence the energy fluxes. Away from the step, the wave evolution of the transmitted and reflected waves is simulated by the Korteweg-de Vries equation. Specific calculations are made using a three-layer fluid model. Three different regimes based on the layer thicknesses are examined and discussed in detail for either depression or elevation mode-1 incident waves. The common features found are that the transmitted waves (mainly mode-1) are the dominant part; most of the incident energy is transmitted and only a small part is reflected. The amplitudes of the generated mode-2 waves and the reflected mode-1 waves increase when either the upper- or middle-layer thickness increases. When the lower layer is thin enough, the amplitude of the transmitted mode-2 wave can be larger than the mode-1 waves, and the reflected energy can increase considerably which we infer may be due to a blocking effect of the step on the lower layer. The evolution away from the step is either fission into several solitary waves, or the development of a rarefaction wave followed by an undular bore, depending on the relative signs of the wave amplitudes and the nonlinear coefficient in the Korteweg-de Vries equation.Vortex-wave interaction on the surface of a spherehttps://zbmath.org/1521.760722023-11-13T18:48:18.785376Z"Nelson, Rhodri B."https://zbmath.org/authors/?q=ai:nelson.rhodri-b"McDonald, N. Robb"https://zbmath.org/authors/?q=ai:mcdonald.n-robbSummary: The time-dependent interaction of a point vortex with a vorticity jump separating regions of opposite signed and constant vorticities on the surface of a non-rotating sphere is examined. First, small amplitude interfacial waves are considered where linear theory is applicable. A point vortex in a region of same-signed vorticity will initially move away from the interface and a point vortex in a region of opposite-signed vorticity will move towards it. Weak vortices sufficiently far from the interface then undergo meridional oscillation while precessing about the sphere. The sense of azimuthal precession is determined by the sign of the vorticity jump at the interface. It is demonstrated by both linear and nonlinear theories that a vortex at a pole in a region of same-signed vorticity is a stable equilibrium whereas a vortex at a pole in a region of opposite-signed vorticity is an unstable equilibrium. Numerical computations using contour dynamics confirm these results and the dynamics of more nonlinear cases are examined.The nonlinear evolution of internal tides. II: Lagrangian transport by periodic and modulated waveshttps://zbmath.org/1521.760752023-11-13T18:48:18.785376Z"Sutherland, Bruce R."https://zbmath.org/authors/?q=ai:sutherland.bruce-r"Yassin, Houssam"https://zbmath.org/authors/?q=ai:yassin.houssamSummary: We examine Lagrangian transport by a nonlinearly evolving vertical mode-1 internal tide in non-uniform stratification. In a companion paper [the authors, ibid. 948, Paper No. A21, 22 p. (2022; Zbl 1521.76074)] it was shown that a parent internal tide can excite successive superharmonics that superimpose to form a solitary wave train. Despite this transformation, here we show that the collective forcing by the parent wave and superharmonics is effectively steady in time. Thus we derive relatively simple formulae for the Stokes drift and induced Eulerian flow associated with the waves under the assumption that the parent waves and superharmonics are long compared with the fluid depth. In all cases, the Stokes drift exhibits a mixed mode-1 and mode-2 vertical structure with the flow being in the waveward direction at the surface. If the background rotation is non-negligible, the vertical structure of the induced Eulerian flow is equal and opposite to that of the Stokes drift. This flow periodically increases and decreases at the inertial frequency with maximum magnitude twice that of the Stokes drift. When superimposed with the Stokes drift, the Lagrangian flow at the surface periodically changes from positive to negative over one inertial period. If the background rotation is zero, the induced Eulerian flow evolves non-negligibly in time and space for horizontally modulated waves: the depth below the surface of the positive Lagrangian flow becomes shallower ahead of the peak of the amplitude envelope and becomes deeper in the lee of the peak. These predictions are well-captured by fully nonlinear numerical simulations.Three-dimensional buoyant hydraulic fractures: constant release from a point sourcehttps://zbmath.org/1521.761012023-11-13T18:48:18.785376Z"Möri, Andreas"https://zbmath.org/authors/?q=ai:mori.andreas"Lecampion, Brice"https://zbmath.org/authors/?q=ai:lecampion.briceSummary: Hydraulic fractures propagating at depth are subjected to buoyant forces caused by the density contrast between fluid and solid. This paper is concerned with the analysis of the transition from an initially radial fracture towards an elongated buoyant growth -- a critical topic for understanding the extent of vertical hydraulic fractures in the upper Earth crust. Using fully coupled numerical simulations and scaling arguments, we show that a single dimensionless number governs buoyant hydraulic fracture growth, namely the dimensionless viscosity of a radial hydraulic fracture at the time when buoyancy becomes of order 1. It quantifies whether the transition to buoyancy occurs when the growth of the radial hydraulic fracture is either still in the regime dominated by viscous flow dissipation or already in the regime where fracture energy dissipation dominates. A family of fracture shapes emerge at late time from finger-like (toughness regime) to inverted elongated cudgel-like (viscous regime). Three-dimensional toughness-dominated buoyant fractures exhibit a finger-like shape with a constant-volume toughness-dominated head and a viscous tail having a constant uniform horizontal breadth: there is no further horizontal growth past the onset of buoyancy. However, if the transition to buoyancy occurs while in the viscosity-dominated regime, both vertical and horizontal growths continue to match scaling arguments. As soon as the fracture toughness is not strictly zero, horizontal growth stops when the dimensionless horizontal toughness becomes of order 1. The horizontal breadth follows the predicted scaling.Asymptotic scale-dependent stability of surface quasi-geostrophic vortices: semi-analytic resultshttps://zbmath.org/1521.761352023-11-13T18:48:18.785376Z"Badin, G."https://zbmath.org/authors/?q=ai:badin.gualtiero"Poulin, F. J."https://zbmath.org/authors/?q=ai:poulin.francis-jSummary: The scale-dependent stability of surface quasi-geostrophic (SQG) vortices is studied both analytically and numerically. In particular, we study the sensitivity of the stability of SQG vortices on a nondimensional number \(\sigma\), namely the square root of the Burger number, which sets the transition scale between different dynamical regimes corresponding to local and nonlocal dynamics. We analyse the stability of two different examples. The first example is given by a Rankine vortex, characterised by constant buoyancy. For this case, asymptotic analysis suggests that the frequencies of the perturbations at scales smaller than the transition scale show a \(\sigma^{-1}\) dependence. At scales larger than the transition scale, the frequencies scale instead like \(\sigma^{-2}\). The second example consists of a Rankine vortex shielded by a filament characterised by a different value of constant buoyancy. For this example we study the dispersion relation for the perturbations for the cases in which the inner vortex and the outer filament have different asymptotic properties behaviour.Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applicationshttps://zbmath.org/1521.764182023-11-13T18:48:18.785376Z"Ferrand, Martin"https://zbmath.org/authors/?q=ai:ferrand.martin"Harris, Jeffrey C."https://zbmath.org/authors/?q=ai:harris.jeffrey-cSummary: For reasons of efficiency and accuracy, water wave propagation is often simulated with potential or inviscid models rather than Navier-Stokes solvers, but for wave-induced flows, such as wave-structure interaction, viscous effects are important under certain conditions. Alternatively, general purpose Navier-Stokes (CFD) models can have limitations when applied to such free-surface problems when dealing with large amplitude waves, run-up, or propagation over long distances. Here we present an Arbitrary Lagrangian-Eulerian (ALE) algorithm with special care to the time-stepping and boundary conditions used for the free-surfaces, integrated into \textit{Code\_Saturne}, and we test its capabilities for modeling a variety of water wave generation and propagation benchmarks, and finally consider interaction with a vertical cylinder. Two variants of the mesh displacement computation are proposed and tested against the discrete Geometric Conservation Law (GCL). The more robust variant, for highly curved or sawtoothed free-surfaces, uses a Compatible Discrete Operator scheme on the dual mesh for solving the mesh displacement, which makes the algorithm valid for any polyhedral mesh. Results for standard wave propagation benchmarks for both variants show that, when care is taken to avoid grids with excessive numerical dissipation, this approach is effective at reproducing wave profiles as well as forces on bodies.Boundary element method for wave trapping by a multi-layered trapezoidal breakwater near a sloping rigid wallhttps://zbmath.org/1521.765072023-11-13T18:48:18.785376Z"Khan, Mohamin B. M."https://zbmath.org/authors/?q=ai:khan.mohamin-b-m"Behera, Harekrushna"https://zbmath.org/authors/?q=ai:behera.harekrushna"Sahoo, Trilochan"https://zbmath.org/authors/?q=ai:sahoo.trilochan"Neelamani, S."https://zbmath.org/authors/?q=ai:neelamani.sSummary: This study examines the multiple layers in a rubble mound breakwater and their effect on reflection and dissipation of incoming ocean waves. The numerical model is developed using multi-domain boundary element method for oblique water wave trapping near a sloping wall by a multi-layered trapezoidal porous structure, which is utilized to model armour, filter and core layers while examining the hydrodynamics in different configurations. Both, the constant element and linear element approaches to boundary element method are discussed. The cases of bottom-standing porous structures as being submerged and fully extended are considered. The wave hydrodynamics over the structure is described by the reflection and dissipation coefficients along with the forces acting on the sloping wall, and is influenced by wave and structural parametrics of the system. The influence of armour layer in different configurations is highlighted for various structural and wave parameters.A 3D boundary element method for analysing the hydrodynamic performance of a land-fixed oscillating water column devicehttps://zbmath.org/1521.765112023-11-13T18:48:18.785376Z"Medina Rodríguez, Ayrton Alfonso"https://zbmath.org/authors/?q=ai:medina-rodriguez.ayrton-alfonso"Silva Casarín, Rodolfo"https://zbmath.org/authors/?q=ai:silva-casarin.rodolfo"Blanco Ilzarbe, Jesús María"https://zbmath.org/authors/?q=ai:blanco-ilzarbe.jesus-maria(no abstract)Generalized finite difference method based meshless analysis for coupled two-phase porous flow and geomechanicshttps://zbmath.org/1521.765622023-11-13T18:48:18.785376Z"Liu, Yina"https://zbmath.org/authors/?q=ai:liu.yina"Rao, Xiang"https://zbmath.org/authors/?q=ai:rao.xiang"Zhao, Hui"https://zbmath.org/authors/?q=ai:zhao.hui.3"Zhan, Wentao"https://zbmath.org/authors/?q=ai:zhan.wentao"Xu, Yunfeng"https://zbmath.org/authors/?q=ai:xu.yunfeng"Liu, Yuan"https://zbmath.org/authors/?q=ai:liu.yuan.1|liu.yuan(no abstract)Computation of free surface waves in coastal waters with SWASH on unstructured gridshttps://zbmath.org/1521.766152023-11-13T18:48:18.785376Z"Zijlema, Marcel"https://zbmath.org/authors/?q=ai:zijlema.marcelSummary: This paper aims to present the extension of the non-hydrostatic wave-flow model SWASH with the covolume method to build discretization schemes on unstructured triangular grids. Central to this method that is free of spurious pressure modes, is the use of dual pairs of meshes that are mutually orthogonal, such as the Delaunay-Voronoi mesh systems. The approximants sought are the components of the flow velocity vector normal to the cell faces of the primal mesh. In addition to the covolume approach, a novel upwind difference scheme for the horizontal advection terms in the momentum equation is proposed. This scheme obeys the Rankine-Hugoniot jump relations and prevents the odd-even decoupling of the velocity field accordingly. Moreover, cases with flow discontinuities, such as steady bores and broken waves, are properly treated. In spite of the low-order accuracy of the proposed method, unstructured meshes easily allow for local refinement in a way that retains the desired accuracy. The unstructured-grid version of SWASH is applicable to a wide range of 2DH wave-flow problems to investigate the nonlinear dynamics of free surface waves over varying bathymetries. Its efficiency and robustness is tested on a number of these problems employing unstructured triangular meshes.Estimating the size of the regular region of a topographically trapped vortexhttps://zbmath.org/1521.766212023-11-13T18:48:18.785376Z"Ryzhov, E. A."https://zbmath.org/authors/?q=ai:ryzhov.evgeny-a|ryzhov.eugene-a"Koshel, K. V."https://zbmath.org/authors/?q=ai:koshel.konstantin-vSummary: We formulate a dynamically consistent two-layer quasigeostrophic model of geophysical flow using the concept of background currents which are characterized by a constant potential vorticity minimizing the energy. An incident current over a delta-like isolated topographic feature generates a topographically trapped vortex in the bottom layer with a singular elliptic point, and one with a regular elliptic point in the upper layer. Such vortices are finite regions of recirculation which occur in the vicinity of isolated topographic features. The corresponding Hamiltonian equations of motion for a fluid particle are known to produce chaotic advection under the presence of the periodic incident current. When a periodic incident current is superimposed, fluid is entrained and detrained from the neighbourhood of the vortex and chaotic particle motion occurs. At a small amplitude periodic incident current we have a near-integrable case of weak chaotization in narrow stochastic layer near separatrix. At a finite amplitude periodic incident current we have the case of strong chaos, which will be investigated here. For the bottom layer of the flow, there is always a regular region (regular vortex core) around the singular elliptical point even in the case of a finite amplitude periodic incident current. Particles in this regular region have regular trajectories and will remain there permanently, whereas particles with chaotic trajectories will be emanated from the vortex by the incident current. Using the Chirikov criterion of resonance overlap, we estimate the radius of this regular vortex core and a range of the optimal frequencies, i.e. those frequencies of the incident current which provide a maximal possible stochastization of fluid particle trajectories.Numerical simulation of submarine non-rigid landslide by an explicit three-step incompressible smoothed particle hydrodynamicshttps://zbmath.org/1521.766632023-11-13T18:48:18.785376Z"Hosseini Mobara, Seyed Erfan"https://zbmath.org/authors/?q=ai:hosseini-mobara.seyed-erfan"Ghobadian, Rasool"https://zbmath.org/authors/?q=ai:ghobadian.rasool"Rouzbahani, Fardin"https://zbmath.org/authors/?q=ai:rouzbahani.fardin"Đorđević, Dejana"https://zbmath.org/authors/?q=ai:dordevic.dejanaSummary: Deformable landslide body is modeled as a rheological material when SPH methods are used for numerical simulations. To increase accuracy, Carreau-Yasuda rheological model is chosen in this study. The model overcomes the weakness of the power-law model in predicting viscosity at zero and infinite shear strain rates. Also, a fully explicit three-step algorithm is proposed to solve governing equations. In the \textit{first step}, intermediate velocities are computed in the presence of body forces. In the \textit{second step} , they are used to compute divergence of stress tensor and to find intermediate particle positions. In the \textit{third step}, pressure gradient in the momentum equation is merged with the continuity equation, and final particle velocity is calculated at the end of the time step. The algorithm is used in combination with Carreau-Yasuda model to simulate submarine non-rigid landslide. Comparison with experimental data indicates good agreement between calculated and observed water surface elevations with very low L2 relative error norm \((\varepsilon_{L2})\) and RMSE values. They are up to 70\% lower than those from previous studies when Cross and Bingham rheological models were used with ISPH and WCSPH models, respectively. Moreover, shape and advancement of the non-rigid body made of sand are well captured.Large deformation analysis of geomaterials using stabilized total Lagrangian smoothed particle hydrodynamicshttps://zbmath.org/1521.766672023-11-13T18:48:18.785376Z"Islam, Md Rushdie Ibne"https://zbmath.org/authors/?q=ai:ibne-islam.md-rushdie"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.265"Peng, Chong"https://zbmath.org/authors/?q=ai:peng.chong(no abstract)A comparative study of the cumulant lattice Boltzmann method in a single-phase free-surface model of violent flowshttps://zbmath.org/1521.766962023-11-13T18:48:18.785376Z"Sato, Kenta"https://zbmath.org/authors/?q=ai:sato.kenta"Kawasaki, Koji"https://zbmath.org/authors/?q=ai:kawasaki.koji"Koshimura, Shunichi"https://zbmath.org/authors/?q=ai:koshimura.shunichiSummary: Many coastal and ocean engineering flows, such as tsunamis inundating urban areas, tend to be violent. The characteristics of these damaging flow fields are three-dimensional, highly non-linear and non-hydrostatic. A fully three-dimensional free-surface fluid model is required to simulate such a flow field. Fluid simulations in the field of coastal engineering are often large-scale since large areas are the subject of the simulations. The numerical model must be not only accurate but also efficient. In recent years, the lattice Boltzmann method (LBM) has attracted much attention as a novel simulation method and has been successfully applied to various engineering fields. The LBM calculates complex phenomena in a simple framework. The density field determines the pressure field with the equation of state. This means that the LBM does not have to solve the pressure Poisson equation. However, the existing gas-liquid multi-phase flow models that employ the LBM have a critical problem. Pressure calculations with large density ratios easily become unstable, and the application of these models to violent flow fields is limited. The single-phase free-surface fluid model provides good approximations for flow problems in which the gas dynamics can be neglected. Moreover, the cumulant LBM has attracted attention because it has excellent numerical stability even for high Reynolds number flows. The single-phase free-surface flow model using the cumulant LBM is a suitable approach for simulating violent flow fields in coastal engineering. In this study, we propose a single-phase free-surface flow model based on the cumulant LBM using the volume-of-fluid (VOF) model to capture the interface. We demonstrate that the cumulant LBM is stable under violent flows and reproduces the density field well compared with the traditional single relaxation time model. We find that a larger bulk viscosity can reduce the numerical oscillation of the impact pressure acting on a structure, although a bulk viscosity that is too large reduces the accuracy and stability. The results of the proposed model are in good agreement with previous experimental results.Statistical properties of an enstrophy conserving finite element discretisation for the stochastic quasi-geostrophic equationhttps://zbmath.org/1521.767282023-11-13T18:48:18.785376Z"Bendall, Thomas M."https://zbmath.org/authors/?q=ai:bendall.thomas-m"Cotter, Colin J."https://zbmath.org/authors/?q=ai:cotter.colin-johnSummary: A framework of variational principles for stochastic fluid dynamics was presented by Holm, and these stochastic equations were also derived by Cotter, Gottwald and Holm. We present a conforming finite element discretisation for the stochastic quasi-geostrophic equation that was derived from this framework. The discretisation preserves the first two moments of potential vorticity, i.e. the mean potential vorticity and the enstrophy. Following the work of Dubinkina and Frank, who investigated the statistical mechanics of discretisations of the deterministic quasi-geostrophic equation, we investigate the statistical mechanics of our discretisation of the stochastic quasi-geostrophic equation. We compare the statistical properties of our discretisation with the Gibbs distribution under assumption of these conserved quantities, finding that there is an agreement between the statistics under a wide range of set-ups.A meshless weak strong form method for the groundwater flow simulation in an unconfined aquiferhttps://zbmath.org/1521.767412023-11-13T18:48:18.785376Z"Das, Sanjukta"https://zbmath.org/authors/?q=ai:das.sanjukta"Eldho, T. I."https://zbmath.org/authors/?q=ai:eldho.t-i(no abstract)Groundwater flow simulation in a confined aquifer using local radial point interpolation meshless method (LRPIM)https://zbmath.org/1521.767572023-11-13T18:48:18.785376Z"Swetha, K."https://zbmath.org/authors/?q=ai:swetha.k"Eldho, T. I."https://zbmath.org/authors/?q=ai:eldho.t-i"Singh, L. Guneshwor"https://zbmath.org/authors/?q=ai:singh.laishram-guneshwor|guneshwor-singh.l"Kumar, A. Vinod"https://zbmath.org/authors/?q=ai:kumar.a-vinodSummary: Groundwater flow problems are generally solved using analytical or numerical methods. Though analytical solutions are exact and preferable, they are not available for complex field problems. Hence numerical methods such as Finite Element and Finite Difference methods are used to solve complex groundwater problems. These conventional mesh/ grid-based numerical methods need construction of a detailed mesh/ grid. On the other hand, the meshless approach creates a system of algebraic equations on a collection of distributed nodes in the problem area and the boundary. As a result, it is easy to incorporate any modifications to the model at a later time by simply adding nodes to the domain. In this study a weak form meshless method known as local radial point interpolation method (LRPIM) which uses radial basis functions for approximation or interpolation is developed to solve the groundwater flow problems in a confined aquifer. The results obtained from the LRPIM model has been compared with other numerical methods for benchmark and real field problems, and are found to be satisfactory. Implementation of the essential boundary conditions was relatively easier in LRPIM and gave good accuracy for the problems considered. LRPIM can potentially be used as an alternative to the other conventional methods, especially where the domain boundary is irregular or varying with time.On influence acoustic radiation on electric double layer in ion mediumhttps://zbmath.org/1521.768092023-11-13T18:48:18.785376Z"Shaĭdurov, Georgiĭ Ya."https://zbmath.org/authors/?q=ai:shaidurov.georgii-ya"Romanova, Galina N."https://zbmath.org/authors/?q=ai:romanova.galina-n"Yarygina, Ol'ga L."https://zbmath.org/authors/?q=ai:yarygina.olga-lSummary: This article describes process in double electrical layer on interface electric and ion medium. There are quantitative estimate effects eventuate with communication electromagnetic and acoustic fluctuation on double electrical layer Gui-Gelmgolz.Extended kinetic theory for granular flow in a vertical chutehttps://zbmath.org/1521.768792023-11-13T18:48:18.785376Z"Islam, Mudasir Ul"https://zbmath.org/authors/?q=ai:islam.mudasir-ul"Jenkins, J. T."https://zbmath.org/authors/?q=ai:jenkins.james-t.1"Das, S. L."https://zbmath.org/authors/?q=ai:das.sovan-lalSummary: We consider steady, fully-developed flows of deformable, inelastic grains driven by gravity between identical bumpy walls. Using constitutive relations from extended kinetic theory (EKT) for the erodible bed near the centreline and the collisional flow between the surfaces of the bed and the walls, we calculate the fields of mean velocity, fluctuation velocity and solid volume fraction across the chute. We consider both situations in which the solid volume fraction at and near the centreline is high enough to form a bed and when it is not. We compare results predicted by EKT with recent discrete element simulations results, and obtain very good agreement.Transport and emergent stratification in the equilibrated eady model: the vortex-gas scaling regimehttps://zbmath.org/1521.768912023-11-13T18:48:18.785376Z"Gallet, Basile"https://zbmath.org/authors/?q=ai:gallet.basile"Miquel, Benjamin"https://zbmath.org/authors/?q=ai:miquel.benjamin"Hadjerci, Gabriel"https://zbmath.org/authors/?q=ai:hadjerci.gabriel"Burns, Keaton J."https://zbmath.org/authors/?q=ai:burns.keaton-j"Flierl, Glenn R."https://zbmath.org/authors/?q=ai:flierl.glenn-r"Ferrari, Raffaele"https://zbmath.org/authors/?q=ai:ferrari.raffaeleSummary: We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasigeostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The `vortex gas' scaling predictions put forward in the context of the two-layer QG model carry over to this fully three-dimensional system: the functional dependence of the meridional flux on the control parameters is the same, the two adjustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional heat flux is depth-independent. The vertical heat flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical heat flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical heat fluxes, and of the emergent stratification, without additional fitting parameters.Numerical modelling of turbulent geophysical flows using a hyperbolic shear shallow water model: application to powder snow avalancheshttps://zbmath.org/1521.768922023-11-13T18:48:18.785376Z"Ivanova, Kseniya"https://zbmath.org/authors/?q=ai:ivanova.kseniya"Caviezel, Andrin"https://zbmath.org/authors/?q=ai:caviezel.andrin"Bühler, Yves"https://zbmath.org/authors/?q=ai:buhler.yves"Bartelt, Perry"https://zbmath.org/authors/?q=ai:bartelt.perrySummary: In this work we apply a mathematical model developed by \textit{V. M. Teshukov} [Prikl. Mekh. Tekh. Fiz. 48, No. 3, 8--15 (2007; Zbl 1150.76335); translation in J. Appl. Mech. Tech. Phys. 48, No. 3, 303--309 (2007)] to simulate turbulent powder snow avalanches. The two-parameter model describes the production of turbulent energy from shearing. This energy is associated with the formation of small and large vortices which provide avalanches with their distinctive billow and cleft-like structures. The model accurately predicts the concentration of translational kinetic energy at the avalanche front and likewise the formation of an almost stationary turbulent wake. The calculation of turbulent energy can be exploited to improve air-entrainment and turbulent drag models and therefore to improve engineering calculations of powder cloud height, speed and density, an important problem in snow avalanche mitigation. In present work we focus on the one-dimensional case. The governing equations are discretized with a finite volume second order Godunov-type scheme using HLLC Riemann solver. A good agreement between numerical solution of the new model and the photogrammetric measurements (height, length and frequency of billows, depths of clefts) is observed both at the front and tail of the avalanche for two different data sets.Mathematical background of the Riga dynamo experimenthttps://zbmath.org/1521.769032023-11-13T18:48:18.785376Z"Gailitis, Agris"https://zbmath.org/authors/?q=ai:gailitis.agrisSummary: The Riga dynamo experiment is a laboratory model of the natural process that is responsible for all environmental magnetic-fields which are generated without human interference. This applies to the field of the Earth, the Sun, stars, and even galaxies which are produced by intense motions of large volumes of good electro-conducting fluids. For our experiment, we use molten sodium -- the best liquid electro-conductor available in the laboratory. Approximately \(2\,\mathrm{m}^3\) of molten sodium are filled into a prolonged cylinder, at the top of which rotates a propeller powered by 200 kW from two motors. The cylinder is divided by thin coaxial inner walls into three parts: in the inner tube the propeller moves the sodium flow helically downward; in the middle one the sodium flows vertically upward; and the outer part contains liquid sodium at rest. When the propeller speed exceeds a critical value (depending on temperature: around 1800 rpm, corresponding to a sodium flow of \(0.6\,\mathrm{m}^3\,\mathrm{s}^{-1}\)) then a magnetic-field is spontaneously excited. The field pattern slowly rotates around the vertical axis. To enable self-excitation, the sodium flow had been carefully optimized. This article gives an historical overview about the steps in the mathematical description of the Riga dynamo and the optimization of the sodium flow structure. Our analytical model builds on the Ponomarenko configuration, which we modify in four analytical steps. Firstly, the Ponomarenko model was adopted for finite \(Rm\). Then, instead of real generation, we find convective amplification. Secondly, when the outer conductor was replaced with a return tube an absolute instability was attained but at high \(Rm\). Thirdly, to lower \(Rm\) a third, immobile conductor was inserted outside and all sizes optimized to achieve global generation at minimum \(Rm\). Adopting these sizes, an experiment was designed and made. Fourthly and finally, the velocity profile was replaced by a trial polynomial to identify the direction in which the flow structure should be corrected.Evolution of aligned states within nonlinear dynamoshttps://zbmath.org/1521.769092023-11-13T18:48:18.785376Z"Miller, D."https://zbmath.org/authors/?q=ai:miller.d-claire|miller.david-r|miller.donald-l|miller.david-donald|miller.david-a-b|miller.david-f|miller.donald-g|miller.dawson|miller.david-l|miller.dale-d|miller.david-s|miller.donald-w|miller.damon-a|miller.d-michael|miller.david-marshall|miller.douglas-j|miller.douglas-a|miller.donald-m|miller.daniel-a|miller.darlene|miller.donald-s|miller.david-w|miller.duane-d|miller.donald-j|miller.david-p|miller.daniel-j|miller.douglas-e|miller.douglas-s|miller.david-john|miller.daniel-n|miller.dale-a|miller.daniel-e|miller.david-c|miller.douglas-l|miller.dorothy-jSummary: The Archontis dynamo is a rare example of an MHD dynamo within which forcing drives a dynamo where the flow and magnetic fields are almost perfectly aligned and the energies are approximately equal. In this paper, I expand upon our knowledge of the dynamo by showing that the intermediate steady states of the kinetic and magnetic energies observed by Cameron and Galloway are not a necessary feature of aligned dynamos. Furthermore, I show that the steady state into which the flow and magnetic fields eventually evolve is remarkably robust to the addition of time dependence and asymmetry to the forcing.New energy and helicity bounds for knotted and braided magnetic fieldshttps://zbmath.org/1521.769142023-11-13T18:48:18.785376Z"Ricca, Renzo L."https://zbmath.org/authors/?q=ai:ricca.renzo-lSummary: In this article we present a review of some of the author's most recent results in topological magnetohydrodynamics (MHD), with an eye to possible applications to astrophysical flows and solar coronal structures. First, we briefly review basic work on magnetic helicity and linking numbers, and fundamental relations with magnetic energy and average crossing numbers of magnetic systems in ideal conditions. In the case of magnetic knots, we focus on the relation between their groundstate energy and topology, discussing the energy spectrum of tight knots in terms of \textit{ropelength}. We compare this spectrum with the one given by considering the bending energy of such idealized knots, showing that curvature information provides a rather good indicator of magnetic energy contents. For loose knots far from equilibrium we show that inflexional states determine the transition to braid form. New lower bounds for tight knots and braids are then established. We conclude with results on energy-complexity relations for systems in presence of dissipation.Simulation of Maxwell equation based on an ADI approach and integrated radial basis function-generalized moving least squares (IRBF-GMLS) method with reduced order algorithm based on proper orthogonal decompositionhttps://zbmath.org/1521.780162023-11-13T18:48:18.785376Z"Ebrahimijahan, Ali"https://zbmath.org/authors/?q=ai:ebrahimijahan.ali"Dehghan, Mehdi"https://zbmath.org/authors/?q=ai:dehghan.mehdi"Abbaszadeh, Mostafa"https://zbmath.org/authors/?q=ai:abbaszadeh.mostafa(no abstract)Wind instability of gravitation waves on liquid surface in finite poolhttps://zbmath.org/1521.830252023-11-13T18:48:18.785376Z"Gestrin, S. G."https://zbmath.org/authors/?q=ai:gestrin.s-g"Staravoytova, E. V."https://zbmath.org/authors/?q=ai:staravoytova.e-v(no abstract)Spin-orbit gravitational locking -- an effective potential approachhttps://zbmath.org/1521.850022023-11-13T18:48:18.785376Z"Clouse, Christopher"https://zbmath.org/authors/?q=ai:clouse.christopher"Ferroglia, Andrea"https://zbmath.org/authors/?q=ai:ferroglia.andrea"Fiolhais, Miguel C. N."https://zbmath.org/authors/?q=ai:fiolhais.miguel-c-nSummary: The objective of this paper is to study the tidally locked 3:2 spin-orbit resonance of Mercury around the Sun. In order to achieve this goal, the effective potential energy that determines the spinning motion of an ellipsoidal planet around its axis is considered. By studying the rotational potential energy of an ellipsoidal planet orbiting a spherical star on an elliptic orbit with fixed eccentricity and semi-major axis, it is shown that the system presents an infinite number of metastable equilibrium configurations. These states correspond to local minima of the rotational potential energy averaged over an orbit, where the ratio between the rotational period of the planet around its axis and the revolution period around the star is fixed. The configurations in which this ratio is an integer or an half integer are of particular interest. Among these configurations, the deepest minimum in the average potential energy corresponds to a situation where the rotational and orbital motion of the planet are synchronous, and the system is tidally locked. The next-to-the deepest minimum corresponds to the case in which the planet rotates three times around its axis in the time that it needs to complete two orbits around the Sun. The latter is indeed the case that describes Mercury's motion. The method discussed in this work allows one to identify the integer and half-integer ratios that correspond to spin-orbit resonances and to describe the motion of the planet in the resonant orbit.Oscillatory path integrals for radio astronomyhttps://zbmath.org/1521.850032023-11-13T18:48:18.785376Z"Feldbrugge, Job"https://zbmath.org/authors/?q=ai:feldbrugge.job"Pen, Ue-Li"https://zbmath.org/authors/?q=ai:pen.ueli"Turok, Neil"https://zbmath.org/authors/?q=ai:turok.neil-gSummary: We introduce a new method for evaluating the oscillatory integrals which describe natural interference patterns. As an illustrative example of contemporary interest, we consider astrophysical plasma lensing of coherent sources like pulsars and fast radio bursts in radio astronomy. Plasma lenses are known to occur near the source, in the interstellar medium, as well as in the solar wind and the earth's ionosphere. Such lensing is strongest at long wavelengths, hence it is generally important to go beyond geometric optics and into the full wave optics regime.
Our computational method is a spinoff of new techniques two of us, and our collaborators, have developed for defining and performing Lorentzian path integralswith applications in quantum mechanics, condensed matter physics, and quantum gravity. Cauchy's theorem allows one to transform a computationally fragile and expensive, highly oscillatory integral into an exactly equivalent sum of absolutely and rapidly convergent integrals which can be evaluated in polynomial time. We require only that it is possible to analytically continue the lensing phase, expressed in the integrated coordinates, into the complex domain. We give a first-principles derivation of the Fresnel-Kirchhoff integral, starting from Feynman's path integral for a massless particle in a refractive medium. We then demonstrate the effectiveness of our method by computing the detailed diffraction patterns of Thom's caustic catastrophes, both in their ``normal forms'' and within a variety of more realistic, local lens models, for all wavelengths. Our numerical method, implemented in a freely downloadable code, provides a fast, accurate tool for modeling interference patterns in radioastronomy and other fields of physics.The dynamics of two interacting compositional plumes in the presence of a magnetic fieldhttps://zbmath.org/1521.850082023-11-13T18:48:18.785376Z"Al-Lawatia, M. A."https://zbmath.org/authors/?q=ai:al-lawatia.m-a"Elbashir, T. B. A."https://zbmath.org/authors/?q=ai:elbashir.t-b-a"Eltayeb, I. A."https://zbmath.org/authors/?q=ai:eltayeb.ibrahim-a"Rahman, M. M."https://zbmath.org/authors/?q=ai:rahman.m-muhammad-mahboob-ur|rahman.m-mahibbur|rahman.md-mizanor|rahman.m-m-hafizur|rahman.md-mostafizur|rahman.md-muktadir|rahman.m-mahbubur|rahman.mohammad-muntasir|rahman.md-muklesur|rahman.mohammad-mansur|rahman.mohammad-mafizur|rahman.md-mazder|rahman.m-matiar|rahman.md-mizanur|rahman.md-monsur|rahman.mohammad-mamunur|rahman.m-majedur|rahman.muhammad-m|rahman.md-mashiar|rahman.mohammad-mahabubur|rahman.md-motiur|rahman.md-mijanur|rahman.md-mahmudur|rahman.m-mazibar"Balakrishnan, E."https://zbmath.org/authors/?q=ai:balakrishnan.easwaranSummary: The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied in the presence of a uniform magnetic field, \(\mathbf{B}_0\). The fluid is thermally stably stratified and has a viscosity, \(\nu\), a thermal diffusivity, \(\kappa\) and magnetic diffusivity, \(\eta\). The stability of the mean state to infinitesimal disturbances is governed by the seven dimensionless parameters: the Reynolds number, \(R\) (\(= UL/\nu\), where \(U\), \(L\) are characteristic velocity and length respectively) which measures the strength of the compositional buoyancy; the dimensionless measures \(x_0\), \(x_1\), \(d\) of the thickness of the two plumes and the distance between them, respectively; the ratio \(\Gamma\) of the strengths of the two plumes (as measured by their basic concentration of light material); the Chandrasekhar number, \(Qc\) (\(= B_0^2L^2/\mu\rho_0\eta\nu\), in which \(\mu\) is the magnetic permeability, \(\rho_0\) the fluid density and \(B_0\) a characteristic unit of magnetic field), is a measure of the magnitude of the magnetic field and the normalized horizontal projection \(\hat{B}_H = \sin\theta\) of the magnetic field, where \(\theta\) measures the inclination of the magnetic field to the vertical. The stability is examined for small values of \(R\). The preferred mode of instability is studied in the parameter space \((x_0, x_1, d, \Gamma, Qc, \hat{B}_H)\). It is shown that the influence of the magnetic field does not change the order of the magnitude of the growth rate from \(\mathrm{O}(R^0)\) of the two non-magnetic interacting plumes and it does not introduce any new modes to the stability problem. However, the presence of the magnetic field introduces novel features to the stability problem. For any fixed set \(x_0\), \(x_1\), \(d\), \(\Gamma\), \(Qc\), the growth rate can either increase with \(\hat{B}_H\) or initially decrease reaching a minimum before it increases again. As \(Qc\) increases, with \(x_0\), \(x_1\), \(d\), \(\Gamma\), \(\hat{B}_H\) fixed, the growth rate can assume one of four different behaviour: (i) it maintains the same value of the non-magnetic case with the disturbance propagating along field lines; (ii) it decreases steadily with \(Qc\); (iii) it maintains the same value as in the absence of the field until a value \(Qcm(x_0, x_1, d, \Gamma, \hat{B}_H)\) is reached when it starts to increase to a maximum before it decreases to zero for large values of \(Qc\) and (iv) it increases from its value for \(Qc = 0\) reaching a maximum before it decreases steadily to zero at some value of \(Qc\) dependent on the other parameters. The helicity and \(\alpha\)-effect have also been studied to find that the unstable motions can produce mean helicity and \(\alpha\)-effect.Chaotic behaviour in low-order models of planetary and stellar dynamoshttps://zbmath.org/1521.850152023-11-13T18:48:18.785376Z"Weiss, N. O."https://zbmath.org/authors/?q=ai:weiss.nigel-oSummary: The behaviour of the geodynamo and the solar cycle can be modelled by low-order systems of coupled nonlinear differential equations. The Earth's magnetic field reverses aperiodically, and similar behaviour is exhibited by disc dynamos that are described by the Lorenz equations. Chaotic behaviour is also a characteristic feature of coupled disc dynamos. In stars like the Sun, magnetic activity varies cyclically, with regular reversals of magnetic fields, but the cyclic activity is modulated on longer timescales. This behaviour can be described by normal form equations that account for symmetry-breaking as well as for variations in amplitude. The Von Kármán Sodium (VKS) experiment has successfully demonstrated magnetic reversals in the laboratory, and these results can be represented by evolution equations also.High order instabilities of the Poincaré solution for precessionally driven flowhttps://zbmath.org/1521.860012023-11-13T18:48:18.785376Z"Wu, Cheng-Chin"https://zbmath.org/authors/?q=ai:wu.cheng-chin"Roberts, Paul H."https://zbmath.org/authors/?q=ai:roberts.paul-hSummary: Sloudsky in 1895 and Poincaré in 1910 were the first to derive solutions for the flow driven in the Earth's fluid core by the luni-solar precession. In 1993, Kerswell investigated the stability of this so-called ``Poincaré flow'' by applying a method devised in 1992 by Ponomarev and Gledzer to study the instability of flows with elliptical streamlines. They represented the components of the perturbed flow by sums of polynomials. Kerswell restricted attention to the linear and quadratic cases. Here cubic, quartic, quintic, and sextic generalizations are developed. Instabilities are located in new areas of parameter space, including some that verge on the small oblateness of the Earth's coreA steady azimuthal stratified flow modelling the antarctic circumpolar currenthttps://zbmath.org/1521.860022023-11-13T18:48:18.785376Z"Abrashkin, A. A."https://zbmath.org/authors/?q=ai:abrashkin.a-a"Constantin, A."https://zbmath.org/authors/?q=ai:constantin.adrian|constantin.alexandre|constantin.andreiSummary: We investigate steady flow moving purely in the azimuthal direction on a rotating sphere and having a meridionally localized jet structure. An exact solution for a stratified inviscid fluid, which admits a depth-dependent velocity profile below the surface, is constructed in spherical coordinates. This solution is relevant to the modelling of the Antarctic Circumpolar Current. We show that the stratification enables us to dispense with the nonconservative body force that was invoked in recent spherical-coordinate models to produce realistic flow profiles.Surface semi-geostrophic dynamics in the oceanhttps://zbmath.org/1521.860032023-11-13T18:48:18.785376Z"Badin, G."https://zbmath.org/authors/?q=ai:badin.gualtieroSummary: The surface quasi-geostrophic approximation is re-written in an oceanic context using the two-dimensional semi-geostrophic approximation. The new formulation allows to take into account the presence of out-of-balance flow features at scales comparable to or smaller than the Rossby radius of deformation and for small bulk Richardson numbers. Analytical solutions show that, while the surface quasi-geostrophic approximation tends to underestimate the buoyancy anomaly, the inclusion of finite Rossby number allows for larger values of the buoyancy anomaly at depth. The projection of the surface semi-geostrophic solution on the first baroclinic modes is calculated. The result of the projection is a functional form that decreases with the values of the Rossby number and toward smaller scales. Solutions for constant and exponential profile for the background potential vorticity are compared. Results of the comparison show that, in agreement with the results found for balanced flows, even for large Rossby number the exponential profile for the background potential vorticity retains smaller values for the buoyancy anomaly at depth than the solution found using a constant potential vorticity profile.An eddifying Stommel model: fast eddy effects in a two-box oceanhttps://zbmath.org/1521.860042023-11-13T18:48:18.785376Z"Barham, William"https://zbmath.org/authors/?q=ai:barham.william"Grooms, Ian"https://zbmath.org/authors/?q=ai:grooms.ian-gSummary: A system of stochastic differential equations is formulated describing the heat and salt content of a two-box ocean. Variability in the heat and salt content and in the thermohaline circulation between the boxes is driven by fast Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability. The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian noise. The qualitative effects of this non-Gaussianity are investigated by comparing to two approximate models: one that includes only the mean eddy effects (the ``averaged model''), and one that includes an additional Gaussian white-noise approximation of the eddy effects (the ``Gaussian model''). Both of these approximate models are derived using the methods of fast averaging and homogenisation. In the parameter regime where the dynamics has a single stable equilibrium the averaged model has too little variability. The Gaussian model has accurate second-order statistics, but incorrect skew and rare-event probabilities. In the parameter regime where the dynamics has two stable equilibria the eddy noise is much smaller than the atmospheric noise. The averaged, Gaussian, and non-Gaussian models all have similar stationary distributions, but the jump rates between equilibria are too small for the averaged and Gaussian models.Ocean circulations driven by meridional density gradientshttps://zbmath.org/1521.860052023-11-13T18:48:18.785376Z"Bell, Michael J."https://zbmath.org/authors/?q=ai:bell.michael-jSummary: State-of-the-art ocean models spinning up from realistic density fields rapidly develop deep western boundary currents and meridional overturning circulations (MOCs). \textit{R. Wajsowicz} and \textit{A. E. Gill} [Adjustment of the ocean under buoyancy forces, Part I: The role of Kelvin waves. J. Phys. Oceanogr. 16, 2097--2114 (1986)] found that the initial spin-up of a flat-bottomed ocean model from a meridionally varying density field is well described by the shallow water equations for a two-layer fluid and that the initial evolution on a \(\beta\)-plane could be understood in terms of \(f\)-plane dynamics: Kelvin waves propagate rapidly round the ocean boundaries establishing eastern and western boundary currents. The time-mean baroclinic motion of a two-layer fluid in a closed basin on an \(f\)-plane which spins up from an initial state of rest with a meridionally sloping interface is derived here and compared with Gill's steady-state solution [\textit{A. E. Gill}, Adjustment under gravity in a rotating channel, J. Fluid Mech. 77, 603--621 (1977)] for an open channel. These solutions are used to illustrate the constraints imposed by the no normal flow inviscid boundary conditions which also apply to solutions on a sphere or \(\beta\)-plane. Miles' solution [\textit{J. W. Miles}, Kelvin waves on oceanic boundaries.
J. Fluid Mech. 55, 113--127 (1972; Zbl 0244.76006)] for Kelvin waves on a sphere is used to analyse the initial spin-up on a \(\beta\)-plane. Motivated by the slow speed of the geostrophic adjustment by the planetary waves at mid- to high-latitudes and the influence of the inviscid boundary conditions, simple, analytical steady-state solutions driven by relaxation of the internal interface towards a meridionally varying reference field and closed by dissipative boundary layers are derived using the planetary geostrophic equations for the baroclinic motion in a two-layer fluid. The solutions can be applied to basins which span the equator and derived using the full nonlinear continuity equation for any shape of basin. The depth of the internal interface is constant along the eastern boundaries and the equator but its east-west variations can be a large fraction of the pole to equator difference at high latitudes. The solutions support significant MOCs and, when periodic east-west boundary conditions are imposed at the southern boundary, can be shown to have a significant cross-equatorial baroclinic flow in the western boundary layer with greater southward flow in the lower layer than the surface layer.Linear baroclinic and parametric instabilities of boundary currentshttps://zbmath.org/1521.860062023-11-13T18:48:18.785376Z"Carton, Xavier"https://zbmath.org/authors/?q=ai:carton.xavier-j"Poulin, FrancisJ."https://zbmath.org/authors/?q=ai:poulin.francisj"Pavec, Marc"https://zbmath.org/authors/?q=ai:pavec.marcSummary: The linear baroclinic and parametric instabilities of boundary currents with piecewise-constant potential vorticity are studied in a two-layer quasi-geostrophic model. The growth rates of both the exponential modes and of the optimal perturbations are calculated for the baroclinic instability of steady coastal currents. We show that the growth rates of the exponential modes are maximal for a vertically symmetric flow. Furthermore, the vertical asymmetries induced by different layer thicknesses, the presence of a barotropic potential vorticity or bottom topography, all act to dampen the growth rates and favor growth at shorter wavelengths. It is shown that this behavior can be predicted from the conditions for vertical resonance of Rossby waves on the two potential vorticity fronts. Also, the baroclinic instability of the optimal perturbations has larger growth rates at shorter wavelengths and shorter time scales. As well, the presence of a sloping bottom of moderate amplitude favors the growth of these optimal perturbations. Finally, we compute the growth rates of parametric instability of oscillatory coastal flows. We show that subharmonic resonance is the most unstable mode of growth. In addition, a second region of parametric instability is found (for the first time) away from marginality of exponential-mode baroclinic instability. It is shown that the functional dependency of the growth rates of parametric instability, for optimal excitation, are similar to that of the optimal perturbations of baroclinic instability. To explain this a mechanism for parametric instability, involving the rapid growth of short-wave optimal perturbations, is proposed.Water waves generated by instantaneous disturbances at the bed of a sloping beachhttps://zbmath.org/1521.860072023-11-13T18:48:18.785376Z"Chakraborty, Rumpa"https://zbmath.org/authors/?q=ai:chakraborty.rumpa"Mandal, B. N."https://zbmath.org/authors/?q=ai:mandal.birendra-nathSummary: The two-dimensional problem of the generation of water waves due to instantaneous disturbances prescribed at the bed of a beach sloping at an arbitrary angle is studied here. It is formulated in terms of an initial-boundary-value problem for the velocity potential describing the motion in the fluid region assuming the linear theory. Using the Laplace transform in time and the Mellin transform in distance, the problem is reduced to solving a difference equation whose method of solution is of considerable importance in the literature. The form of the free surface is obtained in terms of a multiple infinite integral that is evaluated by the method of steepest-descent. For some prescribed forms of the disturbance at the bed of the beach, the free surface is depicted in a number of figures for different beach angles. It is observed that as the beach angle decreases, the maximum wave height increases, which is plausible.Improved bounds on linear instability of barotropic zonal flow within the shallow water equationshttps://zbmath.org/1521.860082023-11-13T18:48:18.785376Z"Clark, A. D."https://zbmath.org/authors/?q=ai:clark.antwan-d|clark.allan-derek"Herron, I. H."https://zbmath.org/authors/?q=ai:herron.isom-h-junSummary: Here we develop mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water. The bottom topography is taken to be one-dimensional and the isobaths are parallel to the mean flow. In the case of a rotating fluid, the isobaths and the mean flow are assumed to be zonal. The flow is front-like: there is a monotonic increase of mean flow velocity. Our results show that for barotropic flows the location of instabilities will be a semi-ellipse region in the complex wave velocity plane, that is based on the wave-number, Froude number, and depth of the fluid layer. We also explore the instability region for the case of spatially unbounded mean velocity profiles for non-rotating shallow water.Bay-trapped low-frequency oscillations in lakeshttps://zbmath.org/1521.860092023-11-13T18:48:18.785376Z"Johnson, E. R."https://zbmath.org/authors/?q=ai:johnson.edward-r"Kaoullas, G."https://zbmath.org/authors/?q=ai:kaoullas.georgeSummary: Observations of thermocline variation in long lakes have shown oscillations with periods of several days concentrated at the lake ends. These have been attributed to resonances of topographic shelf-wave reflection. Here a complementary description is presented showing how the presence of a shallow bay region at a lake end raises the maximum allowable frequency for locally propagating shelf-wave modes above the maximum for waves in the absence of the bay and thus leads to trapping of energy at frequencies lying between these two maxima.Modelling the process of non-equilibrium hydrate formation in a porous reservoirhttps://zbmath.org/1521.860102023-11-13T18:48:18.785376Z"Khasanov, Marat Kamilovich"https://zbmath.org/authors/?q=ai:khasanov.marat-kamilovich"Kildibaeva, Svetlana Rustamovna"https://zbmath.org/authors/?q=ai:kildibaeva.svetlana-rustamovna"Stolpovskiĭ, Maksim Vladimirovich"https://zbmath.org/authors/?q=ai:stolpovskii.maksim-vladimirovichSummary: This paper presents a solution to the flat-dimensional problem of gas hydrate formation in a porous medium. Highly permeable reservoirs are considered, as a result of which it is assumed that the process accompanied by the transition of gas into the hydrate composition is nonequilibrium. Based on the numerical solution, the influence of injection pressure and formation permeability on the peculiarities of phase transitions process has been studied. It is shown that with an increase in the injection pressure, both the maximum possible temperature of the system and the length of the hydrate-containing region increase. It has been found that the maximum temperature realized in the system, depending on the permeability of the reservoir, has a non-monotonic character. The influence of the initial temperature of the porous reservoir on the dynamics of phase transitions has been studied.Ocean turbulence at meso and submesoscales: connection between surface and interior dynamicshttps://zbmath.org/1521.860112023-11-13T18:48:18.785376Z"Klein, Patrice"https://zbmath.org/authors/?q=ai:klein.patrice"Lapeyre, Guillaume"https://zbmath.org/authors/?q=ai:lapeyre.guillaume"Roullet, Guillaume"https://zbmath.org/authors/?q=ai:roullet.guillaume"Le Gentil, Sylvie"https://zbmath.org/authors/?q=ai:le-gentil.sylvie"Sasaki, Hideharu"https://zbmath.org/authors/?q=ai:sasaki.hideharuSummary: High resolution simulations of ocean turbulence with Rossby number of order one have revealed that upper layer dynamics significantly differs from the interior dynamics. As reported before, upper layer dynamics is characterized with shallow velocity spectrum corresponding to kinetic energy distributed over a spectral range from mesoscales to small scales. This dynamics is driven by small-scale frontogenesis related to surface density anomalies. Interior dynamics is characterized by steeper velocity spectrum and is driven by the potential vorticity anomalies set up by the interior baroclinic instability. Impact of the divergent motions related to surface frontogenesis leads to a warming of the upper layers, a cyclone dominance and a negative skewness of the isopycnal displacements. On the contrary, divergent motions in the interior lead to a cooling of the deeper layers, an anticylone dominance and a positive skewness of the isopycnal displacements. These different ageostrophic processes are consistent with an SQG regime extended to Rossby number of order one on one hand and an interior QG regime extended to Rossby number of order one on the other hand, as proposed by previous studies. Synthesis of these characteristics suggest a connection between upper and deeper layers, induced by the divergent motions, through which small scales near the surface interact with mesoscales in the interior.An analytic benchmark test for karst-aquifer flowhttps://zbmath.org/1521.860122023-11-13T18:48:18.785376Z"Loper, David E."https://zbmath.org/authors/?q=ai:loper.david-eSummary: A benchmark test for flow in karstic aquifers is presented in the form of an exact solution of the harmonic variations of water flux and head within a karst conduit that is imbedded within a three-dimensional porous matrix having a free surface. The variations are driven by a prescribed variation of head applied at one end of the conduit. The benchmark consists of expressions for the spring discharge as a function of time and the conduit head and flux as functions of distance along the conduit and time. These expressions contain three dimensionless parameters, permitting development of a wide range of specific benchmark tests. The expressions are particularly simple in the case of an infinitely deep aquifer. This limiting solution should provide the most severe test for two-dimensional models of karst aquifer flow. Another limiting case of interest is that in which the conduit diameter is equal to the water depth. This limiting solution should provide the easiest test for two-dimensional models.Influence of a deep flow on a surface boundary currenthttps://zbmath.org/1521.860132023-11-13T18:48:18.785376Z"Meunier, T."https://zbmath.org/authors/?q=ai:meunier.thomas"Carton, X. J."https://zbmath.org/authors/?q=ai:carton.xavier-j"Duarte, R."https://zbmath.org/authors/?q=ai:duarte.rui.1Summary: The stability properties of a coastal current composed of a deep flow and of an intense counterflowing surface jet are investigated with a linear quasi-geostrophic model and with a nonlinear isopycnic shallow-water model (MICOM), both in three-layer configurations. The currents are modeled by strips of uniform potential vorticity anomaly (PVA), with opposite signs. The linear stability analysis of the current is performed with exponentially-growing modes, varying the ratio of layer thicknesses, the potential vorticity distribution (width and intensity of the PVA strips) and the perturbation wavelength. The effect of a sloping bottom is also investigated. The various nonlinear regimes are described and interpreted in terms of growth of the modal perturbations, of critical layer distributions and of interactions of PVA poles. The linear growth rates of the perturbations are essential for enough PVA of the currents to reach the critical layers before wave breaking can occur. The positions of the critical layers determine where cut-off of the PVA contours occurs. This position is shown to depend only on the lower layer thickness (the upper layer one being kept constant). The intermediate layer thickness determines only the growth rates of the perturbation. Finally, the long-time nonlinear evolutions are governed by the interaction of detached PVA poles. An oceanographic application is performed using a 4-layer configuration, representative of the Mediterranean water undercurrents flowing under the South Portugal coastal upwelling jet. The analysis of this configuration shows that even for a stable upper layer, instability-driven eddies in the lower layers can disturb the surface jet and generate large meanders and filaments, similar to the observations from south of the Iberian peninsula.Baroclinic multipole evolution in shear and strainhttps://zbmath.org/1521.860142023-11-13T18:48:18.785376Z"Sokolovskiy, Mikhail A."https://zbmath.org/authors/?q=ai:sokolovskiy.mikhail-a"Koshel, Konstantin V."https://zbmath.org/authors/?q=ai:koshel.konstantin-v"Carton, Xavier"https://zbmath.org/authors/?q=ai:carton.xavier-jSummary: In a two-layer quasi-geostrophic model, the evolution of a symmetric baroclinic multipole, composed of a central vortex with strength \(\mu\kappa\) in the upper layer, and \(A\) satellites with strength \(\kappa\) in the lower layer, is studied. This multipole is imbedded in a center-symmetric shear/strain field, either steady or time-periodic. Special attention is given to the case of the tripole (\(A = 2\)). The stability of this tripole is assessed and its oscillations in the external field are analyzed. Conditions for resonance of these oscillations are derived and transition to chaos is described.Internal Kelvin wave frontogenesis on the equatorial pycnoclinehttps://zbmath.org/1521.860152023-11-13T18:48:18.785376Z"Stepanov, DmitryV."https://zbmath.org/authors/?q=ai:stepanov.dmitryv"Novotryasov, Vadim"https://zbmath.org/authors/?q=ai:novotryasov.vadimSummary: This study investigates the influence of the background stratification of the pycnocline on Kelvin wave frontogenesis on the equatorial beta plane using numerical simulations. The pycnocline is characterized by its depth and thickness. We analyzed the propagation of a nonlinear Kelvin wave on the equatorial pycnocline at different depths and thicknesses. Our numerical simulations show that the steepening of a nonlinear Kelvin wave develops in a similar manner for varying parameters of the pycnocline. We calculated and analyzed the dependence of the time of breaking on the pycnocline at different depths and thicknesses. We found that an increase in the thickness of the pycnocline results in a delay of Kelvin wave frontogenesis. However, an increase in the depth of the pycnocline results in a decrease of the time of the breaking of a nonlinear Kelvin wave. Our numerical results show that the nonlinear Kelvin wave would break after four months of evolution on the equatorial pycnocline in the Pacific Ocean.Deformation and splitting of baroclinic eddies encountering a tall seamounthttps://zbmath.org/1521.860162023-11-13T18:48:18.785376Z"Sutyrin, Georgi"https://zbmath.org/authors/?q=ai:sutyrin.georgi-g"Herbette, S."https://zbmath.org/authors/?q=ai:herbette.steven"Carton, X."https://zbmath.org/authors/?q=ai:carton.xavier-jSummary: The transformation of baroclinic eddies encountering a tall seamount is explored using a three-layer primitive equation model on the \(\beta\)-plane. The topography is finite in that the seamount penetrates the isopycnal layer in which the eddy resides, but does not span the entire fluid depth. In our numerical simulations, the eddies are represented by potential vorticity anomalies in the upper and middle layers, and propagating towards the seamount due to the beta-effect. Circulations created near the topography, both by fluid removed from the seamount and by external fluid stranded over the seamount, play a key role in the drift, deformation, and erosion of the approaching eddies. When the radius of the seamount is small, the deviation of the eddy trajectory is well described by a simple kinematic model that does not take into account deformations of the vortex cores. For wider seamounts, such interactions may result in horizontal and/or vertical splitting of the vortex core, i.e., in increased occurrences of eddy destruction. In particular, an interesting mechanism is found, related to enhancement of topographic circulation by potential vorticity entrained from the vortex core in the middle layer, and resulting in strong deformations and splitting of the upper layer core. Numerical estimates of the transformed eddy structure indicate that topographic interactions provide powerful mechanisms for significantly influencing baroclinic eddy evolution. Our results are summarized in a specific nondimensional parameter space according to the eddy evolution.Flow of grounded abyssal ocean currents along zonally-varying topography on a rotating spherehttps://zbmath.org/1521.860172023-11-13T18:48:18.785376Z"Swaters, Gordon E."https://zbmath.org/authors/?q=ai:swaters.gordon-eSummary: A steady nonlinear planetary-geostrophic model in spherical coordinates is presented describing the hemispheric-scale meridional flow of grounded abyssal currents on a zonally-sloping bottom. The model, which corresponds mathematically to a quasi-linear hyperbolic partial differential equation, can be solved explicitly for a cross-slope isopycnal field that is grounded (i.e. intersects the bottom on the up slope and down slope sides). As a consequence of the conservation of potential vorticity, the abyssal currents possess decreasing thickness in the equatorward direction while maintaining constant meridional volume transport. There is a small westward zonal transport in the interior of these currents that results in westward intensification as they flow toward the equator. Conditions for the possible formation of a shock to develop on the up slope flank of the current are derived.A continuous-discontinuous deformation analysis method for simulating the progressive failure process of riverbankshttps://zbmath.org/1521.860182023-11-13T18:48:18.785376Z"Xu, Dongdong"https://zbmath.org/authors/?q=ai:xu.dongdong"Lu, Bo"https://zbmath.org/authors/?q=ai:lu.bo"Cheng, Yonghui"https://zbmath.org/authors/?q=ai:cheng.yonghui"Zhu, Jiebing"https://zbmath.org/authors/?q=ai:zhu.jiebing"Wang, Bin"https://zbmath.org/authors/?q=ai:wang.bin.23(no abstract)On resonant over-reflection of waves by jetshttps://zbmath.org/1521.860192023-11-13T18:48:18.785376Z"Benilov, E. S."https://zbmath.org/authors/?q=ai:benilov.eugene-s"Lapin, V. N."https://zbmath.org/authors/?q=ai:lapin.vasilii-nikolaevichSummary: It is well known that internal or Rossby waves propagating across a jet can be amplified, a phenomenon usually referred to as over-reflection. In some cases, over-reflection can be infinitely strong -- physically, this means that the reflected and transmitted waves can exist without an incident one, i.e. they are spontaneously emitted by the mean flow. In this article, it is shown that infinitely strong over-reflection (resonant over-reflection) occurs for gravity-wave scattering by ageostrophic jets in a rotating barotropic ocean and Rossby-wave scattering by a two-jet configuration on the quasigeostrophic beta-plane. It is further demonstrated that, generally, a resonantly over-reflected wave is always marginal to instability, i.e. either an increase or a decrease of its wavenumber transforms it into an unstable eigenmode localised near the jet.Effect of stratification on the frequency of bounded Rossby modes over a non-flat bottomhttps://zbmath.org/1521.860202023-11-13T18:48:18.785376Z"Colantuono, Giuseppe"https://zbmath.org/authors/?q=ai:colantuono.giuseppe"Erdélyi, Robert"https://zbmath.org/authors/?q=ai:erdelyi.robert"Ruderman, Michael S."https://zbmath.org/authors/?q=ai:ruderman.michael-sSummary: This work attempts to express and analyze the challenges, induced by stratification, affecting the Rossby-topographic eigenmodes of a closed domain with a general uneven bottom of arbitrary shape filled with a uniform fluid in the unperturbed configuration. The modified eigenmodes have been computed analytically: stratification is introduced in the mathematical form of a perturbation of a homogeneous fluid over a non-flat bottom. The eigenmodes lose their barotropic character and differences appear in the dynamical fields (velocity and pressure) from upper to lower layer, as expected. Expressions for the baroclinic and ageostrophic velocity components due to the perturbation are given. The analysis is carried out in the frame of linear shallow water approximation. All terms have been retained apart from nonlinear advection in the governing equations. We find that the frequencies of the eigenmodes change; an analytical expression of frequency correction as a function of layer density difference and interface depth is found. Initial results for some elementary geometrical settings with a waveguide bottom are determined and expressed in a concise, easily readable closed form. The results obtained in the shallow water approximation are expanded in series with respect to the Rossby number. Next, they are compared with the frequency correction obtained in an alternative framework in which the quasi-geostrophic approximation is used, and a purely baroclinic perturbation is imposed from the outset as the result of the introduction of stratification in the otherwise homogeneous fluid. In this scenario, reduced gravity and the ratio of upper to lower layer depth are, in turn, used as the expansion parameters \textit{in lieu} of the Rossby number.A note on the derivation of the quasi-geostrophic potential vorticity equationhttps://zbmath.org/1521.860212023-11-13T18:48:18.785376Z"Fowler, A. C."https://zbmath.org/authors/?q=ai:fowler.andrew-cSummary: The derivation of the quasi-geostrophic potential vorticity equation of mathematical meteorology is usually done using fairly sophisticated techniques of perturbation theory, but stops short of deriving self-consistently the stratification parameter of the mean atmospheric state. In this note we suggest how this should be done within the confines of the theory, and as a consequence we raise the possibility that the atmosphere could become globally unstable, with dramatic consequences.A variational derivation of the thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximationhttps://zbmath.org/1521.860222023-11-13T18:48:18.785376Z"Gay-Balmaz, François"https://zbmath.org/authors/?q=ai:gay-balmaz.francoisSummary: Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation for moist atmospheric dynamics with rain process and subject to the irreversible processes of viscosity, heat conduction, diffusion, and phase transition. This derivation is based on a general variational formalism for nonequilibrium thermodynamics which extends Hamilton's principle to incorporate irreversible processes. It is valid for any state equation and thus also includes the treatment of the atmosphere of other planets. In this approach, the second law of thermodynamics is understood as a nonlinear constraint formulated with the help of new variables, called thermodynamic displacements, whose time derivative coincides with the thermodynamic force of the irreversible process. In order to cover the case of atmospheric dynamics, the original variational principle is extended in three directions in this paper: the inclusion of the rain process, the inclusion of phase changes, and the treatment of constraints. The variational formulation is written both in the Lagrangian and Eulerian descriptions and can be directly adapted to oceanic dynamics. The proposed variational formulation yields a general approach for the modelling of thermodynamically consistent models in atmospheric dynamics, thereby extending previous variational methods that were restricted to the reversible Hamiltonian case. We illustrate this point, by deriving a moist pseudoincompressible model with general equations of state and subject to the irreversible processes of viscosity, heat conduction, diffusion, and phase transition.Perturbed Rankine vortices in surface quasi-geostrophic dynamicshttps://zbmath.org/1521.860232023-11-13T18:48:18.785376Z"Harvey, B. J."https://zbmath.org/authors/?q=ai:harvey.b-j"Ambaum, M. H. P."https://zbmath.org/authors/?q=ai:ambaum.maarten-h-pSummary: An analytical dispersion relation is derived for linear perturbations to a Rankine vortex governed by surface quasi-geostrophic dynamics. Such a Rankine vortex is a circular region of uniform anomalous surface temperature evolving under quasi-geostrophic dynamics with uniform interior potential vorticity. The dispersion relation is analysed in detail and compared to the more familiar dispersion relation for a perturbed Rankine vortex governed by the Euler equations. The results are successfully verified against numerical simulations of the full equations. The dispersion relation is relevant to problems including wave propagation on surface temperature fronts and the stability of vortices in quasi-geostrophic turbulence.Reflection of an internal wave at an interface representing a rapid increase in viscosityhttps://zbmath.org/1521.860242023-11-13T18:48:18.785376Z"Mchugh, John"https://zbmath.org/authors/?q=ai:mchugh.john-revere|mchugh.john-philip"Grimshaw, Roger"https://zbmath.org/authors/?q=ai:grimshaw.roger-h-jSummary: Internal waves at high altitudes are greatly damped by the drastic increase in molecular viscosity and thermal diffusivity, resulting in important heating and other effects at those altitudes. Here we consider the case where this increase in viscosity is very rapid, idealized as an interface with inviscid flow in the lower layer and constant viscosity in the upper layer. The results show that waves are partially reflected by this interface, with a reflection coefficient that increases monotonically with an increase in the viscosity of the upper layer. This mechanism would have a significant impact on the vertical distribution of thermal energy at high altitudes.Influence of external flow field on the equilibrium state of quasi-geostrophic point vorticeshttps://zbmath.org/1521.860252023-11-13T18:48:18.785376Z"Miyazaki, T."https://zbmath.org/authors/?q=ai:miyazaki.terunobu|miyazaki.takehiro|miyazaki.takeru|miyazaki.takafumi|miyazaki.tadashi|miyazaki.takayuki|miyazaki.takeshi|miyazaki.tomomi|miyazaki.takunari|miyazaki.toshiaki|miyazaki.tsuyoshi|miyazaki.taro|miyazaki.tatsujiro|miyazaki.takashi|miyazaki.tatsuya|miyazaki.teruo|miyazaki.tetsuro|miyazaki.takuya|miyazaki.taeko"Sato, T."https://zbmath.org/authors/?q=ai:sato.toshihiko|sato.tatsuhiro|sato.tomoyuki|sato.takanori|sato.takuya|sato.takeki|sato.teppei|sato.tomomasa|sato.tokui|sato.takaki|sato.takashi|sato.takayuki|sato.tosiya|sato.tetsuya|sato.taisuke|sato.tadanobu|sato.tomoharu|sato.tsukasa|sato.tomokazu|sato.tetsuro|sato.tatsuro|sato.takako|sato.terukiyo|sato.tomoki|sato.takeyoshi|sato.tadakazu|sato.takehiro|sato.toshiro|sato.takuma|sato.takeshige|sato.takeshi|sato.tomoyoshi|sato.takuso|sato.tohru|sato.takehiko|sato.tomohiko|sato.takuji|sato.takamichi|sato.tokushi|sato.takao.1|sato.taiji|sato.toshinori|sato.toshiyuki|sato.takahiro|sato.takami|sato.tadahiko|sato.toru|sato.toshiki|sato.tsuneo"Kimura, H."https://zbmath.org/authors/?q=ai:kimura.hiroshi|kimura.hironobu|kimura.harusato|kimura.herbert|kimura.hidehito|kimura.hidenori|kimura.hiroyuki|kimura.hitosi|kimura.hideyuki|kimura.hiromichi|kimura.hidehiko"Takahashi, N."https://zbmath.org/authors/?q=ai:takahashi.noi|takahashi.norio|takahashi.norihisa|takahashi.norikazu|takahashi.norio.1|takahashi.naomi|takahashi.norihiko|takahashi.naohisa|takahashi.norihiro|takahashi.naoya|takahashi.nobuyoshi|takahashi.nobuyuki|takahashi.nariaki|takahashi.noriyuki|takahashi.nozomu|takahashi.naoto|takahashi.nobuhiro|takahashi.naoshi|takahashi.nobuo|takahashi.nobuyaSummary: The influence of external flow field on the statistical equilibrium state of quasi-geostrophic point vortices (vortex cloud) is investigated numerically. The numerical computations are performed using the fast special-purpose computer for molecular dynamics simulations, MDGRAPE-3. The equilibrium state in otherwise quiescent fluid is axisymmetric, whose radial distribution depends on both the vertical distribution of vortices \(P(z)\) and the total energy of the vortex system \(E\). At a certain critical energy value \(E_c\), the number of microscopic state with a given angular momentum attains its maximum (zero-inverse temperature state), where the radial distribution is Gaussian at any vertical height. When the energy is smaller (\(E < E_c\): positive temperature), the radial distribution becomes flatter than the Gaussian. In contrast, if the energy is higher (\(E > E_c\): negative temperature), the radial distribution becomes sharper showing tighter concentration near the axis of symmetry. If an equilibrium vortex cloud of positive temperature is immersed in the horizontal strain field \(U_e = ey\), \(V_e = ex\), the vortex distribution is stretched in the \(y\)-direction, and the azimuthally averaged radial distribution becomes Gaussian-like. Similarly, when the equilibrium state of positive temperature is immersed in the vertical shear field \(U_\tau = \tau z\), \(V_\tau = 0\), the vortex cloud is tilted in the \(y\)-direction, and the radial distribution becomes Gaussian-like. These findings explain how the internal vorticity distributions inside interacting vortex clouds of positive temperature change to be nearly zero-inverse temperature state.Generalized LSG models with spatially varying Coriolis parameterhttps://zbmath.org/1521.860262023-11-13T18:48:18.785376Z"Oliver, Marcel"https://zbmath.org/authors/?q=ai:oliver.marcel"Vasylkevych, Sergiy"https://zbmath.org/authors/?q=ai:vasylkevych.sergiySummary: In this paper, we derive and study approximate balance models for nearly geostrophic shallow water flow where the Coriolis parameter is permitted to vary across the domain as long as it remains nondegenerate. This situation includes, for example, the \(\beta\)-plane approximation to the shallow water equations at mid-latitudes. Our approach is based on changing configuration space coordinates in the underlying variational principle in such a way that consistent asymptotics in the transformed Lagrangian leads to a degenerate Lagrangian structure. In this paper, we restrict our attention to first-order models. We show that the resulting models can be formulated in terms of an advected potential vorticity with a nonlinear vorticity inversion relation. We study the associated solvability conditions and identify a subfamily of models for which these conditions are satisfied without additional restrictions on the data. Finally, we provide the link between our framework and the theory of constrained Hamiltonian systems.Diagnosing the causes of bias in climate models -- why is it so hard?https://zbmath.org/1521.860272023-11-13T18:48:18.785376Z"Palmer, T. N."https://zbmath.org/authors/?q=ai:palmer.tim-n"Weisheimer, Antje"https://zbmath.org/authors/?q=ai:weisheimer.antjeSummary: The equations of climate are, in principle, known. Why then is it so hard to formulate a bias-free model of climate? Here, some ideas in nonlinear dynamics are explored to try to answer this question. Specifically it is suggested that the climatic response to physically different forcings shows a tendency to project onto structures corresponding to the systems natural internal modes of variability. This is shown using results from complex climate models and from the relatively simple Lorenz three-component model. It is suggested that this behaviour is consistent with what might be expected from the fluctuation-dissipation theorem. Based on this, it is easy to see how climate models can easily suffer from having errors in the representation of two or more different physical processes, whose responses compensate one another and hence make individual error diagnosis difficult. A proposal is made to try to overcome these problems and advance the science needed to develop a bias-free climate model. The proposal utilises powerful diagnostics from data assimilation. The key point here is that these diagnostics derive from short-range forecast tendencies, estimated long before the model has asymptotically settled down to its (biased) climate attractor. However, it is shown that these diagnostics will not identify all sources of model error, and a so-called ``bias of the second kind'' is discussed. This latter bias may be alleviated by recently developed stochastic parametrisations.Polar accumulation of cyclonic vorticityhttps://zbmath.org/1521.860282023-11-13T18:48:18.785376Z"Scott, R. K."https://zbmath.org/authors/?q=ai:scott.richard-kSummary: The drift of coherent vortices on a background gradient of potential vorticity has been previously studied in the case of uniform gradient. Here an extension is made to the case where the background gradient varies with a radial coordinate in an approximation to the variation of planetary potential vorticity on a rotating sphere. It is found that accumulation of cyclonic vorticity at the pole occurs provided the initial vortex anomaly exceeds the polar value of potential vorticity by approximately 12\%. Although polar accumulation becomes slower as the deformation radius decreases, it persists for values as low as about 0.025 of the planetary radius. Polar accumulation of cyclonic vorticity is also found to persist in fully turbulent flows emerging from a large number of coherent vortex anomalies. In this case, a mixed zone in potential vorticity develops in a polar surf zone surrounding the polar cyclone, with a sharp jump at the surf zone edge defining a distinct subpolar jet whose structure depends on the deformation radius. The results are discussed in the context of the coherent polar cyclones and subpolar jets observed on the giant planets.Near-fault broadband seismograms synthesis in a stratified transversely isotropic half-space using a semi-analytical frequency-wavenumber methodhttps://zbmath.org/1521.860292023-11-13T18:48:18.785376Z"Ba, Zhenning"https://zbmath.org/authors/?q=ai:ba.zhenning"Liu, Yue"https://zbmath.org/authors/?q=ai:liu.yue.3"Liang, Jianwen"https://zbmath.org/authors/?q=ai:liang.jianwen"Liu, Jiaqiao"https://zbmath.org/authors/?q=ai:liu.jiaqiao"Niu, Jiaqi"https://zbmath.org/authors/?q=ai:niu.jiaqi(no abstract)Fracture in concrete gravity dams under dynamic loading conditionshttps://zbmath.org/1521.860302023-11-13T18:48:18.785376Z"Lahiri, Saptarshi Kumar"https://zbmath.org/authors/?q=ai:lahiri.saptarshi-kumar"Shaw, Amit"https://zbmath.org/authors/?q=ai:shaw.amit"Ramachandra, L. S."https://zbmath.org/authors/?q=ai:ramachandra.l-s"Maity, Damodar"https://zbmath.org/authors/?q=ai:maity.damodar(no abstract)The scattering of seismic waves from saturated river valley with water layer: modelled by indirect boundary element methodhttps://zbmath.org/1521.860312023-11-13T18:48:18.785376Z"Liu, Zhong-Xian"https://zbmath.org/authors/?q=ai:liu.zhongxian"Ai, Tian-Chun"https://zbmath.org/authors/?q=ai:ai.tian-chun"Huang, Lei"https://zbmath.org/authors/?q=ai:huang.lei"Yuan, Xiao-Ming"https://zbmath.org/authors/?q=ai:yuan.xiaoming"Zhang, Ming-Kai"https://zbmath.org/authors/?q=ai:zhang.ming-kai"Huang, Long"https://zbmath.org/authors/?q=ai:huang.long(no abstract)Three-dimensional IBEM solution to seismic wave scattering by a near-fault sedimentary basinhttps://zbmath.org/1521.860322023-11-13T18:48:18.785376Z"Liu, Zhong-Xian"https://zbmath.org/authors/?q=ai:liu.zhongxian"Huang, Zhen-En"https://zbmath.org/authors/?q=ai:huang.zhen-en"Meng, Si-Bo"https://zbmath.org/authors/?q=ai:meng.si-bo(no abstract)Characteristics of earthquake input energy of a subway station structure based on probability density evolution methodhttps://zbmath.org/1521.860332023-11-13T18:48:18.785376Z"Liu, Z. Q."https://zbmath.org/authors/?q=ai:liu.zi-qiang|liu.zhiqiang|liu.zhiqian|liu.zhiqing|liu.ziqing|liu.zhuoqi|liu.zhaoqian|liu.zhaoqiang|liu.zuoqiu|liu.zhaoqin|liu.zunquan|liu.ziqi|liu.zequn|liu.zhongquan|liu.zhengquan|liu.ziqiu|liu.zhongqiang|liu.zaiqiang|liu.zhongqiu|liu.zaoqing|liu.zongqian|liu.zanqin|liu.zhao-qing|liu.zhenquan|liu.zhenqiu|liu.zhaoqi|liu.ziqiong|liu.zeqing|liu.zhiqiu|liu.zhuqing|liu.zhanqiang|liu.zhiqi|liu.zhenqing|liu.ziqian|liu.zhengqiu"Chen, Z. Y."https://zbmath.org/authors/?q=ai:chen.zhengyang|chen.zuo-yi|chen.zhiyan|chen.zhangyue|chen.zhiyou|chen.zhongyuan|chen.zhangyao|chen.zongyun|chen.zhao-you|chen.zeyu|chen.zhengyi|chen.zhouye|chen.zhiyong|chen.zeyi|chen.zhongyong|chen.zhuoyu|chen.zhongyu|chen.zu-yi|chen.zhanyu|chen.ziyun|chen.zen-yi|chen.zhiya|chen.zhaoyi|chen.zhongyue|chen.zhiyu|chen.zun-yi|chen.zhao-yun|chen.zhen-yong|chen.zhouyang|chen.zi-yue|chen.zih-yin|chen.zhaoyang|chen.zhongying|chen.zuyu|chen.zongyong|chen.zongyuan|chen.ziyi|chen.zhenyue|chen.zhenyu|chen.zhangyuan|chen.zhiyang|chen.zhengyu|chen.zhaoying|chen.zhiyi|chen.zhenyang|chen.zhaoyu|chen.zheyu|chen.zhiyin|chen.zhe-yun|chen.ziyang|chen.zhenyi|chen.zhang-yong|chen.zhiyun|chen.zhiying|chen.zhuoyuan|chen.zhangyou|chen.ziyu|chen.zhiyuan|chen.zhao-yue|chen.zeying|chen.zhiyao|chen.ziyin"Zhao, H."https://zbmath.org/authors/?q=ai:zhao.hu.1Summary: Understanding seismic energy input and dissipation mechanism is necessary for energy-based seismic design of complex underground structures. Due to the intrinsic uncertainty of ground motion, stochastic methods are usually needed. In this paper, we study the seismic energy input and dissipation mechanism in an underground structure using the probability density evolution method (PDEM). It is found that the cumulative hysteretic energy dissipation \(( E_h)\) of the underground structure is reduced by 55\% compared with the above-ground structure due to soil constraint. The columns, walls and slabs at the bottom of the underground structure have a high demand for \(E_h\), which are vulnerable spots of the structure.A novel scaled boundary finite element method for dynamic impedance of an arch dam foundation in a complex layered half-spacehttps://zbmath.org/1521.860342023-11-13T18:48:18.785376Z"Li, Zhi-yuan"https://zbmath.org/authors/?q=ai:li.zhiyuan"Hu, Zhi-qiang"https://zbmath.org/authors/?q=ai:hu.zhiqiang"Hong, Zhong"https://zbmath.org/authors/?q=ai:hong.zhong"Lin, Gao"https://zbmath.org/authors/?q=ai:lin.gaoSummary: This study is devoted to the evaluation of dynamic impedance of the arch dam foundation embedded in a complex layered half-space. For this purpose, a modified scaled boundary finite element method (SBFEM) is developed for modeling the far field. In order to overcome the limits of scaling requirements of the original SBFEM, a scaled boundary transformation based on a scaling surface is developed, which can model the geometry of an infinitely long canyon exactly. Besides, the complex material portions of half-space can also be easily and exactly simulated using the modified scaled boundary transformation. Corresponding to the novel scaled boundary transformation, the governing equations of the modified SBFEM in terms of the displacement and dynamic stiffness are derived based on the frame work of Hamiltonian system. Comparison with existing solutions for a foundation supported on a semi-circular canyon in a homogeneous half-space confirms the accuracy and efficiency of the proposed approach. The effects of horizontal layers, shape of cross-section and the curved axis of canyon are investigated. The results show that the layers of half-space may have a significant effect on the dynamic stiffness of the canyon foundation.Scattering attenuation of transient \textit{SH}-wave by an orthotropic Gaussian-shaped sedimentary basinhttps://zbmath.org/1521.860352023-11-13T18:48:18.785376Z"Mojtabazadeh-Hasanlouei, Saeed"https://zbmath.org/authors/?q=ai:mojtabazadeh-hasanlouei.saeed"Panji, Mehdi"https://zbmath.org/authors/?q=ai:panji.mehdi"Kamalian, Mohsen"https://zbmath.org/authors/?q=ai:kamalian.mohsen(no abstract)Laterally loaded piles and pile groups partially embedded in transversely isotropic fractional viscoelastic saturated soilshttps://zbmath.org/1521.860362023-11-13T18:48:18.785376Z"Ai, Zhi Yong"https://zbmath.org/authors/?q=ai:ai.zhiyong"Wang, Da Shan"https://zbmath.org/authors/?q=ai:wang.da-shan"Zhao, Yong Zhi"https://zbmath.org/authors/?q=ai:zhao.yongzhi"Li, Pan Cong"https://zbmath.org/authors/?q=ai:li.pan-cong(no abstract)Numerical estimation of multiple leakage positions of a marine pollutant using the adjoint marginal sensitivity methodhttps://zbmath.org/1521.860372023-11-13T18:48:18.785376Z"Kanao, Shunsuke"https://zbmath.org/authors/?q=ai:kanao.shunsuke"Sato, Toru"https://zbmath.org/authors/?q=ai:sato.toruSummary: When abnormally high concentration of a pollutant is observed in the ocean, it is very important to search for leakage positions and fluxes of the pollutant. To reduce time and expense of such search effort in the ocean, a numerical method was proposed for estimating a leakage position and its flux using a limited number of observed concentration data. This method is called the adjoint marginal sensitivity method, which is a time-backward probabilistic method to estimate a leakage position and a flux. In this study, we improved the method to deal with multiple leakage positions and validated this newly developed method. In addition, we showed the conditions for successful estimation using the simulation results of a well-planned two-dimensional case studies by changing flow velocity, eddy diffusion coefficient, distance between two leakage positions, spatial observation range, and sensor spacing. Moreover, we applied this method to a three-dimensional case with real topography and obtained reasonably acceptable results, suggesting that the knowledge learnt in the two-dimensional case studies is effective.Mechanisms for magnetic field generation in precessing cubeshttps://zbmath.org/1521.860382023-11-13T18:48:18.785376Z"Goepfert, O."https://zbmath.org/authors/?q=ai:goepfert.o"Tilgner, A."https://zbmath.org/authors/?q=ai:tilgner.andreasSummary: It is shown that flows in precessing cubes develop at certain parameters large axisymmetric components in the velocity field which are large enough to either generate magnetic fields by themselves, or to contribute to the dynamo effect if inertial modes are already excited and acting as a dynamo. This effect disappears at small Ekman numbers. The critical magnetic Reynolds number also increases at low Ekman numbers because of turbulence and small-scale structures.Large-eddy simulations of convection-driven dynamos using a dynamic scale-similarity modelhttps://zbmath.org/1521.860392023-11-13T18:48:18.785376Z"Matsui, Hiroaki"https://zbmath.org/authors/?q=ai:matsui.hiroaki"Buffett, Bruce A."https://zbmath.org/authors/?q=ai:buffett.bruce-aSummary: Dynamo simulations require sub-grid scale (SGS) models for the momentum and heat flux, the Lorentz force, and the magnetic induction. Previous large eddy simulations (LES) using the scale similarity model have represented many aspects of the SGS motion. However, discrepancies are observed due to interchanging the order of filtering operation and spatial differentiation. In this study, we implement a correction term for this commutation error specifically for the scale-similarity model. Furthermore, we implement a dynamic scheme to evaluate time-dependent coefficients for the SGS models. We perform dynamo simulations in a rotating plane layer with different spatial resolutions, and compare results for the time dependence of the large-scale magnetic field. Simulations are performed at two different Rayleigh numbers, using constant values for the other dimensionless numbers (Ekman, Prandtl, and magnetic Prandtl numbers). Both cases show that the dynamic LES can accurately represent the large-scale magnetic field, whereas the dynamo failed in the direct simulations without the SGS terms at the same spatial resolutions. We conclude that the dynamic versions of the SGS and commutation error correction are essential for successful dynamos on coarser grids.Erratum to: ``Large-eddy simulations of convection-driven dynamos using a dynamic scale-similarity model''https://zbmath.org/1521.860402023-11-13T18:48:18.785376Z"Matsui, Hiroaki"https://zbmath.org/authors/?q=ai:matsui.hiroaki"Buffett, Bruce A."https://zbmath.org/authors/?q=ai:buffett.bruce-aFrom the text: The article detailed above, published in [the authors, ibid. 106, No. 3, 250--276 (2012; Zbl 1521.86039)] had errors introduced into it between the iFirst version (published 1 August 2011) and the issue version, namely, equations (2) and (5) did not display and additional line breaks appeared on p. 254.Unstable periodic orbits in a four-dimensional Faraday disk dynamohttps://zbmath.org/1521.860412023-11-13T18:48:18.785376Z"Moroz, Irene M."https://zbmath.org/authors/?q=ai:moroz.irene-mSummary: In this article, we return to a four-dimensional model for a self-exciting Faraday disk dynamo, originally investigated by \textit{R. Hide} and \textit{I. M. Moroz} [Physica D 134, No. 2, 287--301 (1999; Zbl 0949.76095)]. We extract unstable periodic orbits from long time series of chaotic trajectories by the method of close returns to a Poincaré section. We then employ recently developed topological tools to characterise the underlying chaotic attractor of the dynamo by identifying its branched manifold or template.Vector and scalar spherical harmonic spectral equations for rapidly rotating anisotropic alpha-effect dynamoshttps://zbmath.org/1521.860422023-11-13T18:48:18.785376Z"Phillips, C. G."https://zbmath.org/authors/?q=ai:phillips.christopher-gSummary: Spectral equations are derived for a mean field induction equation, \(\partial\overline{\boldsymbol{B}}/\partial t - \nabla^2\overline{\boldsymbol{B}} = R\nabla\times\boldsymbol{F}\) with an \(\boldsymbol{\alpha}\)-effect, considered appropriate for rapid rotation, given by \(\boldsymbol{F} = \boldsymbol{\alpha}\cdot\overline{\boldsymbol{B}} = a_1\overline{\boldsymbol{B}} + a_3\hat{\boldsymbol{z}}\cdot\overline{\boldsymbol{B}}\hat{\boldsymbol{z}}\), where \((\hat{\boldsymbol{x}}, \hat{\boldsymbol{y}}, \hat{\boldsymbol{z}})\) are Cartesian unit vectors, \(a_1(r, \theta, \phi)\), \(a_3(r, \theta, \phi)\) are scalar functions of position, \((r, \theta, \phi)\) are spherical polar coordinates and \(R\) is the magnetic Reynolds number. The effect of rotation on convection for different boundaries and parameters is discussed. The effect of the flow structure on \(\boldsymbol{\alpha}\) for different geostrophic and near geostrophic models is analysed. The vector spherical harmonics
\[
\boldsymbol{Y}^m_{n, n_1}(\theta, \phi) = (-1)^{n-m}[2n+1]^{1/2}\sum\limits_{\mu = -1, 0, 1}\begin{pmatrix} n & n_1 & 1 \\ m & \mu-m & -\mu \end{pmatrix}\mathrm{Y}_{n_1}^{m-\mu}\boldsymbol{e}_\mu,
\]
where \(\boldsymbol{e}_{-1} = (\hat{\boldsymbol{x}}-\mathrm{i}\hat{\boldsymbol{y}})/2^{1/2}\), \(\boldsymbol{e}_0 = \hat{\boldsymbol{z}}\), \(\boldsymbol{e}_1 = -(\hat{\boldsymbol{x}}-\mathrm{i}\hat{\boldsymbol{y}})/2^{1/2}\), the \(2 \times 3\) matrix is a Wigner 3J coefficient and \(\mathrm{Y}^m_n = \mathrm{Y}^m_n(\theta, \phi)\) are scalar spherical harmonics, are used to derive the vector \(\boldsymbol{Y}^m_{n, n_1}\) forms of the induction equation for this \(\boldsymbol{\alpha}\)-effect. The solenoidal condition \(\nabla\cdot\overline{\boldsymbol{B}} = 0\) is imposed by relating the \(\boldsymbol{Y}^m_{n, n_1}\) formalism to the toroidal-poloidal harmonic formalism, \(\boldsymbol{T}^m_n = \nabla\times(\boldsymbol{r}T^m_n\mathrm{Y}^m_n)\) and \(\boldsymbol{S}^m_n = \nabla\times\nabla\times(\boldsymbol{r}S^m_n\mathrm{Y}^m_n)\). The \(T^m_n\) and \(S^m_n\) components of the induction equation are thus derived in terms of \(F^m_{n, n_1}\), the \(\boldsymbol{Y}^m_{n, n_1}\) components of \(\boldsymbol{F}\); \(\boldsymbol{F} = \sum_{n_1=n-1}^{n+1}\sum_{m=-n}^n\sum^\infty_{n=0}F^m_{n, n_1}\boldsymbol{Y}^m_{n. n_1}\). These combined \(T^m_n/\boldsymbol{Y}^m_{n, n_1}\), \(S^m_n/\boldsymbol{Y}^m_{n, n_1}\) vector spectral equations are then transformed into interaction type \((a_{n_a}S_nS_N)_{\mathrm{I}}\), \((a_{n_a}T_nT_N)_{\mathrm{I}}\), \((a_{n_a}S_nT_N)_{\mathrm{I}}\), \((a_{n_a}T_nS_N)_{\mathrm{I}}\) and \((a_{n_a}S_nS_N)_{\mathrm{A}}\), \((a_{n_a}T_nT_N)_{\mathrm{A}}\), \((a_{n_a}S_nT_N)_{\mathrm{A}}\), \((a_{n_a}T_nS_N)_{\mathrm{A}}\) equations for the isotropic and anisotropic components of \(\boldsymbol{\alpha}\). As an application of the general spectral equations derived herein, the interaction equations can be specialised by restricting \(a_1\) and \(a_3\) to be proportional to \(r\cos\theta\) or \(\cos\theta\), or restricting \(\overline{\boldsymbol{B}}\) and \(\boldsymbol{\alpha}\) to be axisymmetric. These equations are then compared to those of previous works. The differences between the equations derived herein and those of past works provide corrections and account for, at least in part, the differences in numerical solutions of the past works.Broken ergodicity, magnetic helicity, and the MHD dynamohttps://zbmath.org/1521.860432023-11-13T18:48:18.785376Z"Shebalin, John V."https://zbmath.org/authors/?q=ai:shebalin.john-vSummary: We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory.The onset of thermo-compositional convection in rotating spherical shellshttps://zbmath.org/1521.860442023-11-13T18:48:18.785376Z"Silva, Luis"https://zbmath.org/authors/?q=ai:silva.luis-g-silva-e|silva.luis-m-a|silva.luis-nuno|silva.luis-o|silva.luis-f-p|silva.luis-carlos"Mather, James F."https://zbmath.org/authors/?q=ai:mather.james-f"Simitev, Radostin D."https://zbmath.org/authors/?q=ai:simitev.radostin-dSummary: Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviour often distinct from that of the single diffusive system. In order to understand how the differences in thermal and compositional molecular diffusivities determine the dynamics of thermo-compositional convection we investigate numerically the linear onset of convective instability in a double-diffusive setup. We construct an alternative equivalent formulation of the non-dimensional equations where the linearised double-diffusive problem is described by an effective Rayleigh number, Ra, measuring the amplitude of the combined buoyancy driving, and a second parameter, \(\alpha\), measuring the mixing of the thermal and compositional contributions. This formulation is useful in that it allows for the analysis of several limiting cases and reveals dynamical similarities in the parameters space which are not obvious otherwise. We analyse the structure of the critical curves in this Ra-\(\alpha\) space, explaining asymptotic behaviour in \(\alpha\), transitions between inertial and diffusive regimes, and transitions between large-scale (fast drift) and small-scale (slow drift) convection. We perform this analysis for a variety of diffusivities, rotation rates and shell aspect ratios showing where and when new modes of convection take place.Small-scale dynamo in Riemannian spaces of constant curvaturehttps://zbmath.org/1521.860452023-11-13T18:48:18.785376Z"Sokoloff, Dmitry"https://zbmath.org/authors/?q=ai:sokolev.dmitry|sokolov.dmitrii-dmitrievich"Rubashny, Alexey"https://zbmath.org/authors/?q=ai:rubashny.alexeySummary: We compare temporal growth of the mean magnetic energy \(\mathcal{E}\) driven by a small-scale dynamo in Euclidean and Lobachevsky spaces. The governing parameters of the dynamo, such as the rms turbulent velocity and the correlation scale of turbulence, are presumed to vary randomly in space so the dynamo growth rate is a Gaussian random field. Since such a field is unbounded in unbounded space and can achieve, with a low probability, very large values of \(\mathcal{E}\), it can grow super-exponentially in both cases. The super-exponential growth of \(\mathcal{E}\) in Euclidean space, known since the 1980s, can be considered as a statement that the mean energy growth rate is determined up to a weakly growing factor proportional to \(\sqrt{\ln t}\). We demonstrate that the super-exponential growth of \(\mathcal{E}\) in Lobachevsky space is a much more radical phenomenon, where \(\mathcal{E}\) grows as \(\exp(\mathrm{const}\times t^{5/3})\). We stress that extrapolating the properties of small-scale dynamos in Euclidean space to curved geometries such Lobachevsky space is not straightforward and requires some care. The effects under discussion becomes however important only if the spatial scale of domain in which the small-scale magnetic field is excited exceeds the radius of curvature.An asymptotic solution of a kinematic \(\alpha\varOmega\)-dynamo with meridional circulationhttps://zbmath.org/1521.860462023-11-13T18:48:18.785376Z"Soward, Andrew M."https://zbmath.org/authors/?q=ai:soward.andrew-m"Bassom, Andrew P."https://zbmath.org/authors/?q=ai:bassom.andrew-p"Kuzanyan, Kirill M."https://zbmath.org/authors/?q=ai:kuzanyan.kirill-m"Sokoloff, Dmitry"https://zbmath.org/authors/?q=ai:sokolov.dmitrii-dmitrievichSummary: Asymptotic methods are used to study a one-dimensional kinematic \(\alpha\varOmega\)-Parker dynamo wave model in the limit when the strength of the \(\alpha\varOmega\)-sources, as measured by the dynamo number \(\mathcal{D}\), is large. The model includes the influence of meridional circulation with a characteristic poleward velocity (strictly a magnetic Reynolds number) \(V\), and builds on the earlier work of \textit{H. Popova} and \textit{D. Sokoloff} [Astron. Nachr. 329, 766--768 (2008; Zbl 1151.85324)]. On increasing \(V\), the equatorward phase velocity of the Parker dynamo wave is decreased and, when a particular value of \(V\) (say \(V_T\propto\mathcal{D}^{1/3}\)) is reached, non-oscillatory solutions ensue. Though a complete analytic solution is not possible for \(V = V_T\), the nature of the transition from travelling waves to non-oscillatory solution, as the value of \(V\) varies across \(V_T\), is readily understood within the asymptotic framework. It is remarkable that such a simple one-dimensional model can illustrate the possibility of either travelling waves or non-oscillatory solutions dependent on the magnitude of the meridional circulation, a feature, which has long been known from the numerical study of the full partial differential equations governing axisymmetric \(\alpha\varOmega\)-dynamos (e.g. \textit{P. H. Roberts} [Kinematic dynamo models. Phil. Trans. R. Soc. Lond. A 272, 663--698 (1972)].Several properties of the model solution after data assimilation into the NEMO Ocean circulation modelhttps://zbmath.org/1521.860472023-11-13T18:48:18.785376Z"Belyaev, K."https://zbmath.org/authors/?q=ai:belyaev.konstantin-p"Kuleshov, A."https://zbmath.org/authors/?q=ai:kuleshov.andrei-aleksandrovich"Smirnov, I."https://zbmath.org/authors/?q=ai:smirnov.ilya-n"Tuchkova, N. P."https://zbmath.org/authors/?q=ai:tuchkova.natalya-pavlovnaSummary: Several characteristics and their dynamics, in particular, sea surface temperature simulated by the ocean circulation model of Nucleus for European Modeling of the Ocean in conjunction with data assimilation using the Generalized Kalman filter method developed by the authors are studied. Numerical simulation has been carried out on the period one month and Agro drifter data were used for assimilation. Argo data were used for different levels from sea surface until 2000 m. The Fokker-Planck-Kolmogorov equation was used to define the confidence bounds of assimilated parameters, in particular, sea surface temperature. The results of numerical experiments have been presented and analysed.Gaussian active learning on multi-resolution arbitrary polynomial chaos emulator: concept for bias correction, assessment of surrogate reliability and its application to the carbon dioxide benchmarkhttps://zbmath.org/1521.860482023-11-13T18:48:18.785376Z"Kohlhaas, Rebecca"https://zbmath.org/authors/?q=ai:kohlhaas.rebecca"Kröker, Ilja"https://zbmath.org/authors/?q=ai:kroker.ilja"Oladyshkin, Sergey"https://zbmath.org/authors/?q=ai:oladyshkin.sergey"Nowak, Wolfgang"https://zbmath.org/authors/?q=ai:nowak.wolfgangSummary: Surrogate models are widely used to improve the computational efficiency in various geophysical simulation problems by reducing the number of model runs. Conventional one-layer surrogate representations are based on global (e.g. polynomial chaos expansion, PCE) or on local kernels (e.g., Gaussian process emulator, GPE). Global representations omit some details, while local kernels require more model runs. The existing multi-resolution PCE is a promising hybrid: it is a global representation with local refinement. However, it can not (yet) estimate the uncertainty of the resulting surrogate, which techniques like the GPE can do. We propose to join multi-resolution PCE and GPE s into a joint surrogate framework to get the best out of both worlds. By doing so, we correct the surrogate bias and assess the remaining uncertainty of the surrogate itself. The resulting multi-resolution emulator offers a pathway for several active learning strategies to improve the surrogate at acceptable computational costs, compared to the existing PCE-kriging approach it adds the multi-resolution aspect. We analyze the performance of a multi-resolution emulator and a plain GPE using didactic test cases and a \(\mathrm{CO_2}\) benchmark, that is representative of many alike problems in the geosciences. Both approaches show similar improvements during the active learning, but our multi-resolution emulator leads to much more stable results than the GPE. Overall, our suggested emulator can be seen as a generalization of multi-resolution PCE and GPE concepts that offers the possibility for active learning.Sensitivity analysis of an air pollution model with using innovative Monte Carlo methods in calculating multidimensional integralshttps://zbmath.org/1521.921002023-11-13T18:48:18.785376Z"Ostromsky, Tzvetan"https://zbmath.org/authors/?q=ai:ostromsky.tzvetan"Todorov, Venelin"https://zbmath.org/authors/?q=ai:todorov.venelin"Dimov, Ivan"https://zbmath.org/authors/?q=ai:dimov.ivan-todor"Georgieva, Rayna"https://zbmath.org/authors/?q=ai:georgieva.raynaSummary: Large-scale models are mathematical models with a lot of natural uncertainties in their input data sets and parameters. Sensitivity analysis (SA) is a powerful tool for studying the impact of these uncertainties on the output results and helps to improve the reliability of these models. In this article we present some results of a global sensitivity study of the Unified Danish Eulerian Model (UNI-DEM). A large number of heavy numerical experiments must be carried out in order to collect the necessary data for such comprehensive sensitivity study. One of the largest supercomputers in Europe and the most powerful in Bulgaria, the petascale EuroHPC supercomputer Discoverer is used to perform efficiently this huge amount of computations.
One of the most important features of UNI-DEM is its advanced chemical scheme, called Condensed CBM IV, which considers a large number of chemical species and all significant reactions between them. The ozone is one of the most harmful pollutants, that is why it is important for many practical applications to study it precisely. Stochastic methods based on Adaptive approach and Sobol sequences are used for computing the corresponding sensitivity measures. We show by experiments that the stochastic algorithms for calculating the multidimensional integrals under consideration are one of the best stochastic techniques for computing the small in value sensitivity indices.
For the entire collection see [Zbl 1511.65004].Note on optimal control problem applied to irrigation with sectioned soilhttps://zbmath.org/1521.921082023-11-13T18:48:18.785376Z"Lemos-Paião, Ana P."https://zbmath.org/authors/?q=ai:lemos-paiao.ana-p"Lopes, Sofia O."https://zbmath.org/authors/?q=ai:lopes.sofia-o"De Pinho, M. D. R."https://zbmath.org/authors/?q=ai:de-pinho.maria-do-rosarioSummary: Assuming that the soil is divided into four sections with respect to its moisture and depth, we propose a new irrigation optimal control problem which consider four state variables: \(x_1\), \(x_2\), \(x_3\) and \(x_4\). The variable \(x_i\) represents the quantity of water in the \(i\)th quarter of the radical depth of the soil, where \(i \in \{1,2,3,4\}\). We consider a single control which represents the flow of water introduced in the soil via its irrigation system, directly on the surface layer. Under the proposed problem, we prove that if the hydrological need of the crop associated with the surface layer is satisfied, then the needs of the other sections are also verified. Moreover, we prove the existence of solution to the proposed problem and we derive the corresponding necessary optimality conditions, in a normal form of the maximum principle. Such conditions allows us to validate (partially) the numerical example.
For the entire collection see [Zbl 1515.93013].Robust nonsingular fixed time terminal sliding mode control for atmospheric pollution detection lidar scanning mechanismhttps://zbmath.org/1521.931672023-11-13T18:48:18.785376Z"Kang, Yu"https://zbmath.org/authors/?q=ai:kang.yu"Yang, Yuxiao"https://zbmath.org/authors/?q=ai:yang.yuxiao"Chen, Cai"https://zbmath.org/authors/?q=ai:chen.cai"Lü, Wenjun"https://zbmath.org/authors/?q=ai:lu.wenjun"Zhao, Yunbo"https://zbmath.org/authors/?q=ai:zhao.yunboSummary: A robust nonsingular fixed time terminal sliding mode control scheme with a time delay disturbance observer is proposed for atmospheric pollution detection lidar scanning mechanism (APDL-SM) system. Distinguished from the conventional terminal sliding mode control methods, the authors design a novel fixed-time terminal sliding surface, the convergence time of sliding mode phase of which has a constant upper bound that is designable by adjusting only one parameter. Moreover, in order to overcome the problem of unknown upper bound of lumped uncertainty including model uncertainty, friction effect and external disturbances from the port environment, the authors propose a time delay disturbance observer to provide an estimation for the system lumped uncertainty. By using the Lyapunov synthesis, the explicit analysis of the convergence time upper bound are performed. Finally, simulation studies are conducted on the APDL-SM system to show the fast convergence rate and strong robustness of the proposed control scheme.