zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Sloshing in a vertical circular cylindrical tank with an annular baffle. II: Nonlinear resonant waves. (English) Zbl 1107.76012

Summary: Weakly nonlinear resonant sloshing in a circular cylindrical baffled tank with a fairly deep fluid depth (depth/radius ratio 1) is examined by using an asymptotic modal method, which is based on Moiseev asymptotic ordering. The method generates a nonlinear asymptotic modal system coupling the time-dependent displacements of linear natural modes. Emphasis is placed on quantifying the effective frequency domains of steady-state resonant waves occurring due to lateral harmonic excitations, versus the size and the location of the baffle. The forthcoming Part 3 will focus on the vorticity stress at the sharp baffle edge and on the related generalisations of the present nonlinear modal system.

[For Part I, see the authors, ibid. 54, 71–88 (2006).]

MSC:
76B10Jets and cavities, cavitation, free-streamline theory, water-entry problems, etc.
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M45Asymptotic methods, singular perturbations (fluid mechanics)
References:
[1]Gavrilyuk I, Lukovsky IA, Trotsenko Yu, Timokha AN (2006) The fluid sloshing in a vertical circular cylindrical tank with an annular baffle. Part 1. Linear fundamental solutions. J Eng Math. 54:71–88 · Zbl 1101.76008 · doi:10.1007/s10665-005-9001-6
[2]Colicchio G (2004) Violent disturbance and fragmentation of free surface. Ph.D. Thesis, School of Civil Engineering and the Environment, University of Southampton, UK
[3]Cariou A, Casella G (1999) Liquid sloshing in ship tanks: acomparative study of numerical simulation. Marine Struct 12:183–198 · doi:10.1016/S0951-8339(99)00026-X
[4]Celebi SM, Akyildiz H (2002) Nonlinear modelling of liquid sloshing in a moving rectangular tank. Ocean Engng 29:1527–1553 · doi:10.1016/S0029-8018(01)00085-3
[5]Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comp Phys 191:448–475 · Zbl 1028.76039 · doi:10.1016/S0021-9991(03)00324-3
[6]Cole HA Jr. (1970) Effects of vortex shedding on fuel slosh damping prediction. NASA Technical Note, NASA TN D-5705, Washington DC, March, 28 pp
[7]Bogoryad IB, Druzhinina GZ (1985) On the damping of sloshing a viscous fluid in cylindrical tank with annular baffle. Soviet Appl Mech 21:126–128
[8]Mikishev GI (1978) Experimental methods in the dynamics of spacecraft. Moscow, Mashinostroenie, 247 pp (in Russian)
[9]Mikishev GI, Churilov GA (1977) Some results on the experimental determining of the hydrodynamic coefficients for cylinder with ribs. In: Bogoryad IB (eds). Dynamics of elastic and rigid bodies interacting with a liquid. Tomsk, Tomsk university, pp. 31–37 (in Russian)
[10]Buzhinskii VA (1998) Vortex damping of sloshing in tanks with baffles. J Appl Math Mech 62:217–224 · doi:10.1016/S0021-8928(98)00028-8
[11]Isaacson M, Premasiri S (2001) Hydrodynamic damping due to baffles in a rectangular tank. Canad. J Civil Engng 28:608–616 · doi:10.1139/cjce-28-4-608
[12]Miles JW (1984) Internally resonant surface waves in circular cylinder. J Fluid Mech 149:1–14 · Zbl 0581.76027 · doi:10.1017/S0022112084002500
[13]Miles JW (1984) Resonantly forces surface waves in circular cylinder. J Fluid Mech 149:15–31 · Zbl 0585.76065 · doi:10.1017/S0022112084002512
[14]Faltinsen OM, Timokha AN (2001) Adaptive multimodal approach to nonlinear sloshing in a rectangular rank. J Fluid Mech 432:167–200
[15]Cho JR, Lee HW (2003) Dynamic analysis of baffled liquid-storage tanks by the structural-acoustic finite element formulation. J Sound Vibr 258:847–866 · doi:10.1006/jsvi.2002.5185
[16]Cho JR, Lee HW (2004) Numerical study on liquid sloshing in baffled tank by nonlinear finite element method. Comp Methods Appl Mech Engng 193:2581–2598 · Zbl 1067.76564 · doi:10.1016/j.cma.2004.01.009
[17]Cho JR, Lee HW (2004) Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank. Int J Num Methods Engng 61:514–531 · Zbl 1075.76568 · doi:10.1002/nme.1078
[18]Cho JR, Lee HW, Ha SY (2005) Finite element analysis of resonant sloshing response in 2-D baffled tank. J Sound Vibr 288:829–845 · doi:10.1016/j.jsv.2005.01.019
[19]Biswal KC, Bhattacharyya SK, Sinha PK (in press) Non-linear sloshing in partially liquid filled containers with baffles Int J Num Methods Engng (in press)
[20]Lukovsky IA (1990) Introduction to the nonlinear dynamics of a limited liquid volume. Kiev, Naukova Dumka, pp 220 (in Russian)
[21]Gavrilyuk I, Lukovsky IA, Timokha AN (2000) A multimodal approach to nonlinear sloshing in a circular cylindrical tank. Hybr Methods Engng 2(4):463–483
[22]Gavrilyuk I, Lukovsky I, Makarov V, Timokha A (2006) Evolutional problems of the contained fluid. Kiev, Publishing House of the Institute of Mathematics of NASU, 233 pp
[23]Faltinsen OM, Rognebakke OF, Lukovsky IA, Timokha AN (2000) Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J Fluid Mech 407:201–234 · Zbl 0990.76006 · doi:10.1017/S0022112099007569
[24]Faltinsen OM, Rognebakke OF, Timokha AN (2003) Resonant three-dimensional nonlinear sloshing in a square base basin. J Fluid Mech 487:1–42 · Zbl 1053.76006 · doi:10.1017/S0022112003004816
[25]Faltinsen OM, Rognebakke OF, Timokha AN (2005) Classification of three-dimensional nonlinear sloshing in a tank with finite depth. J Fluids Struct 20:81–103 · doi:10.1016/j.jfluidstructs.2004.08.001
[26]Hill DH (2003) Transient and steady-state amplitudes of forced waves in rectangular tanks. Phys Fluids 15:1576–1587 · Zbl 1186.76228 · doi:10.1063/1.1569917
[27]Ikeda T, Murakami S (2005) Autoparametric resonances in a structure-fluid interaction system carrying a cylindrical liquid tank. J Sound Vibr 285:517–546 · doi:10.1016/j.jsv.2004.08.015
[28]Ikeda T, Murakami S (2005) Nonlinear random responses of a structure parametrically coupled with liquid sloshing in a cylindrical tank. J Sound Vibr 284:75–102 · doi:10.1016/j.jsv.2004.06.049
[29]Lukovsky IA, Timokha AN (1995) Variational methods in nonlinear dynamics of a limited liquid volume. Kiev, Institute of Mathematics, 400 pp (in Russian)
[30]Rognebakke OF, Faltinsen OM (2003) Coupling of sloshing and ship motions. J Ship Res 47:208–221
[31]Faltinsen OM, Rognebakke OF, Timokha AN (2005) Resonant three-dimensional nonlinear sloshing in a square base basin. Part 2. Effect of higher mode. J Fluid Mech 523:199–218 · Zbl 1065.76023 · doi:10.1017/S002211200400196X
[32]La Rocca M, Mele P, Armenio V (1997) Variational approach to the problem of sloshing in a moving container. J Theoret Appl Fluid Mech 1:280–310
[33]La Rocca M, Sciortino G, Boniforti MA (2000) A fully nonlinear model for sloshing in a rotating container. Fluid Dyn Res 27:23–52 · Zbl 1075.76511 · doi:10.1016/S0169-5983(99)00039-8
[34]Faltinsen OM, Timokha AN (2002) Analytically-oriented approaches to two-dimensional fluid sloshing in a rectangular tank (survey). Proc. Inst. Math. Ukrainian Nat Acad Sci 44:321–345
[35]Abramson HN (1966) The dynamics of liquids in moving containers. NASA Report, SP-106, 467 pp
[36]Bredmose H, Brocchini M, Peregrine DH, Thais L (2003) Experimental investigation and numerical modelling of steep forced water waves. J Fluid Mech 490:217–249 · Zbl 1063.76501 · doi:10.1017/S0022112003005238
[37]Hermann M, Timokha A (2005) Modal modelling of the nonlinear resonant sloshing in a rectangular tank I: A model. Math. Models Methods Appl Sci 15:1431–1458 · Zbl 1098.76012 · doi:10.1142/S0218202505000777
[38]Moore RE, Perko LM (1969) Inviscid fluid flow in an accelerating cylindrical container. J Fluid Mech 22:305–320 · Zbl 0133.43901 · doi:10.1017/S0022112065000769
[39]Perko LM (1969) Large-amplitude motions of liquid-vapour interface in an accelerating container. J Fluid Mech 35:77–96 · Zbl 0159.57201 · doi:10.1017/S0022112069000978
[40]Miles JW (1976) Nonlinear surface waves in closed basins. J Fluid Mech 75:419–448 · Zbl 0333.76004 · doi:10.1017/S002211207600030X
[41]Lukovsky IA (1976) Variational method in the nonlinear problems of the dynamics of a limited liquid volume with free surface. In book: Oscillations of Elastic Constructions with Liquid. Volna, Moscow, pp 260–264 (in Russian)
[42]Hill D, Frandsen J (2005) Transient evolution of weakly nonlinear sloshing waves: an analytical and numerical comparison. J Engng Math 53:187–198 · Zbl 1079.76019 · doi:10.1007/s10665-005-2726-4
[43]Narimanov GS (1957) Movement of a tank partly filled by a fluid: the taking into account of non-smallness of amplitude. J Appl Math Mech (PMM) 21:513–524 (in Russian)
[44]arimanov GS, Dokuchaev LV, Lukovsky IA (1977) Nonlinear Dynamics of flying Apparatus with Liquid. Mashinostroenie, Moscow, 203 pp (in Russian)
[45]z 45. Gavrilyuk I, Lukovsky I, Timokha A (2005) Linear and nonlinear sloshing in a circular conical tank. Fluid Dyn Res 37:399–429 · Zbl 1153.76328 · doi:10.1016/j.fluiddyn.2005.08.004
[46]Moiseyev NN (1958) To the theory of nonlinear oscillations of a limited liquid volume. J. Appl Math Mech 22:860–872 · Zbl 0088.43402 · doi:10.1016/0021-8928(58)90126-6
[47]Bogoljubov NN, Mitropolskii Yu (1961) Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach, New York
[48]Ockendon JR, Ockendon H (1973) Resonant surface waves. J Fluid Mech 59:397–413 · Zbl 0273.76006 · doi:10.1017/S0022112073001618
[49]Ockendon H, Ockendon JR, Waterhouse DD (1996) Multi-mode resonance in fluids. J Fluid Mech 315:317–344 · Zbl 0869.76078 · doi:10.1017/S0022112096002443
[50]Dodge FT, Kana DD, Abramson HN (1965) Liquid surface oscillations in longitudinally excited rigid cylindrical . AIAA J 3:685–695 · Zbl 0129.19501 · doi:10.2514/3.2948
[51]Moiseyev NN, Rumyantsev VV (1968) Dynamic Stability of Bodies Containing Fluid. Springer, New York, 326 pp
[52]Lukovsky IA (2004) Variational methods of solving dynamic problems for fluid-containing bodies. Int Appl Mech 40:1092–1128
[53]Bryant PJ (1989) Nonlinear progressive waves in a circular basin. J Fluid Mech 205:453–467 · doi:10.1017/S0022112089002107
[54]Faltinsen OM, Timokha AN (2002) Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth. J Fluid Mech 470:319–357 · Zbl 1163.76325 · doi:10.1017/S0022112002002112
[55]Hutton RE (1963) An investigation of nonlinear, non-planar oscillations of liquid in cylindrical containers, Technical Notes, NASA, D-1870, Washington, 145–153
[56]Royon-Lebeaud A, Cartellier A, Hopfinger EJ Liquid sloshing and wave breaking in cylindrical and square-base. J Fluid Mech (under consideration)
[57]Faltinsen OM, Rognebakke OF, Timokha AN (2006) Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth. Phys. Fluids 18:Art. No. 012103 1–14
[58]Martel C, Nicolas JA, Vega JM (1998) Surface-wave damping in a brimful circular cylinder. J Fluid Mech 360:213–228 · Zbl 0914.76027 · doi:10.1017/S0022112098008520
[59]Graham JMR (1980) The forces on sharp-edged cylinders in oscillatory flow at low Keulegan-Carpenter numbers. J Fluid Mech 97:331–346 · doi:10.1017/S0022112080002595