zbMATH — the first resource for mathematics

Combined numerical model of tsunami. (Russian. English summary) Zbl 1443.76237
Summary: A numerical model describing dynamics of surface gravity waves and acoustic waves excited in the ocean by small dynamic deformations of the bottom is constructed. The model is based on the linear potential theory. The model represents a combination of two dynamically coupled blocks: deep-water and shallow. The deep-water block solves a three-dimensional problem of potential wave theory in a sigma-spherical coordinates, the shallow block – a two-dimensional problem of shallow water theory in spherical coordinates. Results of testing of the numerical model with use of analytical solution of the problem in the case of flat horizontal bottom are shown. A comparative analysis of results of simulations of tsunamis on November 15, 2006 and January 13, 2007 on the Central Kuril Islands with use of newly constructed and traditional long-wave models is carried out.
76U60 Geophysical flows
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
Full Text: DOI MNR
[1] V.V. Titov, F.I. Gonzalez, H.O. Mofjeld, A.J. Venturato, NOAA Time Seattle Tsunami Mapping Project: Procedures, Data Sources, and Products, NOAA Technical Memorandum OAR PMEL-124, 2003, 21 pp.
[2] F. Imamura, A.C. Yalciner, G. Ozyurt, Tsunami Modelling Manual (TUNAMI model), Revision due on april, 2006, 58 pp.
[3] A.I. Zaytsev, A.G. Chernov, A.C. Yalciner, E.N. Pelinovsky, A.A. Kurkin, MANUAL Tsunami Simulation/Visualization Code NAMI DANCE versions 4.9, 2010
[4] O.V. Bulatov, T.G. Elizarova, “Regularized shallow water equations for numerical simulation of flows with a moving shoreline”, Computational Mathematics and Mathematical Physics, 56:4 (2016), 661-679 · Zbl 1426.76343
[5] M.A. Nosov, “Tsunami waves of seismic origin: The modern state of knowledge”, Izvestiya - Atmospheric and Oceanic Physics, 50:5 (2014), 474-484
[6] F.I. Gonzalez, Ye.A. Kulikov, “Tsunami dispersion observed in the deep ocean”, Tsunamis in the World, Springer Netherlands, 1993, 7-16
[7] S. Glimsdal, G.K. Pedersen, C.B. Harbitz, F. Lovholt, Dispersion of tsunamis: does it really matter?, Nat. Hazards Earth Syst. Sci., 13 (2013), 1507-1526
[8] S. Watada, S. Kusumoto, K. Satake, “Traveltime delay and initial phase reversal of distant tsunamis coupled with the self-gravitating elastic earth”, J. Geophys. Res. Solid Earth, 119 (2014), 4287-4310
[9] B.W. Levin, M.A. Nosov, Physics of Tsunamis, Second Edition, Springer, Cham-Heidelberg-New York-Dordrecht-London, 2016, 388 pp.
[10] P.A. Madsen, R. Murray, O.R. Sorensen, “A new form of the Boussinesq equations with improved linear dispersion characteristics”, Coastal engineering, 15:4 (1991), 371-388
[11] F. Lovholt, G. Pedersen, S. Glimsdal, “Coupling of Dispersive Tsunami Propagation and Shallow Water Coastal Response”, The Open Oceanography Journal, 4 (2010), 71-82
[12] F. Shi, J.T. Kirby, J.C. Harris, J.D. Geiman, S.T. Grilli, “A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation”, Ocean Modelling, 43-44 (2012), 36-51
[13] J. Kim, G.K. Pedersen, F. Lovholt, R.J. LeVeque, “A Boussinesq type extension of the GeoClaw model — a study of wave breaking phenomena applying dispersive long wave models”, Coastal Engineering, 122 (2017), 75-86
[14] M.A. Nosov, “Tsunami generation in compressible ocean”, Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere, 24:5 (1999), 437-441
[15] G.R. Gisler, “Tsunami simulations”, Annu. Rev. Fluid Mech., 40 (2008), 71-90 · Zbl 1230.76014
[16] M. Ewing, I. Tolstoy, F. Press, “Proposed use of the T phase in tsunami warning systems”, Bulletin of the Seismological Society of America, 40:1 (1950), 53-58
[17] E.A. Okal, P.J. Alasset, O. Hyvernaud, F. Schindele, “The deficient T waves of tsunami earthquakes”, Geophysical Journal International, 152:2 (2003), 416-432
[18] M.A. Nosov, S.V. Kolesov, A.V. Ostroukhova, A.B. Alekseev, B.W. Levin, “Elastic oscillations of the water layer in a tsunami source”, Doklady earth sciences, 404 (2005), 1097-1100
[19] M.A. Nosov, S.V. Kolesov, “Elastic oscillations of water column in the 2003 Tokachi-oki tsunami source: in-situ measurements and 3-D numerical modelling”, Nat. Hazards Earth Syst. Sci., 7 (2007), 243-249
[20] W. Li, H. Yeh, K. Hirata, T. Baba, “Ocean-bottom pressure variations during the 2003 Tokachi-Oki Earthquake”, Nonlinear Wave Dynamics, ed. P. Lynett, World Scientic Publishing Co., Singapore, 2009, 109-126 · Zbl 1202.86018
[21] T. Ohmachi, H. Tsukiyama, H. Matsumoto, “Simulation of tsunami induced by dynamic displacement of seabed due to seismic faulting”, Bulletin of the Seismological Society of America, 91:6 (2001), 1898-1909
[22] B.H. Choi, E. Pelinovsky, D.C. Kim, I. Didenkulova, S.B. Woo, “Two- and three-dimensional computation of solitary wave runup on non-plane beach”, Nonlin. Processes Geophys., 15 (2008), 489-502
[23] T. Maeda, T. Furumura, “FDM simulation of seismic waves, ocean acoustic waves, and tsunamis based on tsunami-coupled equations of motion”, Pure Appl. Geophys., 170:1-2 (2013), 109-127
[24] A. Kozelkov, A. Kurkin, E. Pelinovskii, V. Kurulin, “Modeling the cosmogenic tsunami within the framework of the Navier-Stokes equations with sources of different types”, Fluid Dynamics, 50:2 (2015), 306-313 · Zbl 1325.76073
[25] A. Bolshakova, S. Inoue, S. Kolesov, H. Matsumoto, M. Nosov, T. Ohmachi, “Hydroacoustic effects in the 2003 Tokachi-oki tsunami source”, Russ. J. Earth. Sci., 12 (2011), ES2005
[26] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, v. 6, Fluid mechanics, 2nd ed., Pergamon Press, 1987, 539 pp. · Zbl 0655.76001
[27] M.A. Nosov, A.V. Moshenceva, S.V. Kolesov, “Horizontal motions of water in the vicinity of a tsunami source”, Pure Appl. Geophys., 170:9-10 (2013), 1647-1660
[28] M.A. Nosov, A.V. Bolshakova, S.V. Kolesov, “Displaced water volume, potential energy of initial elevation, and tsunami intensity: Analysis of recent tsunami events”, Pure and Applied Geophysics, 171:12 (2014), 3515-3525
[29] A.F. Blumberg, G.L. Mellor, “A description of a three-dimensional coastal ocean circulation model”, Coastal and Estuarine Sciences, 4, ed. N. Heaps, Amer. Geophys. Union, 1987, 1-16
[30] M.A. Nosov, “Adapting a Mesh when Simulating Tsunami Waves”, MM&CS, 10:4 (2018), 431-440 · Zbl 1413.86006
[31] Y. Kaneda, H. Matsumoto, M.A. Nosov, S.V. Kolesov, “Analysis of Pressure and Acceleration Signals from the 2011 Tohoku Earthquake Observed by the DONET Seafloor Network”, Journal of Disaster Research, 12:1 (2017), 163-175
[32] M.A. Nosov, “Tsunami generation in a compressible ocean by vertical bottom motions”, Izvestiya, Atmospheric and Oceanic Physics, 36:5 (2000), 661-669
[33] M.A. Nosov, S.V. Kolesov, “Optimal initial conditions for simulation of seismotectonic tsunamis”, Pure and Applied Geophysics, 168:6-7 (2011), 1223-1237
[34] Y. Okada, “Surface deformation due to shear and tensile faults in a half-space”, Bull. Seis. Soc. Am., 75:4 (1985), 1135-1154
[35] M.A. Nosov, K.A. Sementsov, “Calculation of the initial elevation at the tsunami source using analytical solutions”, Izvestiya - Atmospheric and Oceanic Physics, 50:5 (2014), 539-546
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.