메뉴 건너뛰기




Volumn 12, Issue 3, 2009, Pages 607-621

Nonlinear resonances of water waves

Author keywords

Dynamical systems; Fluid mechanics; Nonlinear resonances

Indexed keywords


EID: 70350634314     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.12.607     Document Type: Article
Times cited : (14)

References (68)
  • 1
    • 33646764519 scopus 로고    scopus 로고
    • Direct numerical simulations of downshift and inverse cascade for water wave turbulence
    • S. Annenkov and V. Shrira, Direct numerical simulations of downshift and inverse cascade for water wave turbulence, Phys. Rev. Lett., 96 (2006), 204501-1-204501-4
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 2045011-2045014
    • Annenkov, S.1    Shrira, V.2
  • 3
    • 84974336691 scopus 로고
    • The disintegration of wavetrains in deep water, Part 1
    • T. B. Benjamin and J. E. Feir, The disintegration of wavetrains in deep water, Part 1, J. Fluid Mech., 27 (1967), 417-431.
    • (1967) J. Fluid Mech. , vol.27 , pp. 417-431
    • Benjamin, T.B.1    Feir, J.E.2
  • 4
    • 79051470447 scopus 로고    scopus 로고
    • Dynamics of nonlinear resonances in Hamiltonian systems
    • M. D. Bustamante and E. Kartashova, Dynamics of nonlinear resonances in Hamiltonian systems, Europhys. Lett., 85 (2009), 14004-1-14004-5
    • (2009) Europhys. Lett. , vol.85 , pp. 140041-140045
    • Bustamante, M.D.1    Kartashova, E.2
  • 5
    • 78951496084 scopus 로고    scopus 로고
    • Effect of the dynamical phases on the nonlinear amplitudes' evolution
    • M. D. Bustamante and E. Kartashova, Effect of the dynamical phases on the nonlinear amplitudes' evolution, Europhys. Lett., 85 (2009), 3402-1-3402-6
    • (2009) Europhys. Lett. , vol.85 , pp. 34021-34026
    • Bustamante, M.D.1    Kartashova, E.2
  • 7
    • 0030184063 scopus 로고    scopus 로고
    • A generalized stability criterion for resonant triad interactions
    • C. C. Chow, D. Henderson and H. Segur, A generalized stability criterion for resonant triad interactions, J. Fluid Mech., 319 (1996), 67-76.
    • (1996) J. Fluid Mech. , vol.319 , pp. 67-76
    • Chow, C.C.1    Henderson, D.2    Segur, H.3
  • 8
    • 79051471430 scopus 로고    scopus 로고
    • Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
    • A. Constantin and E. Kartashova, Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves, Europhys. Lett., 86 (2009), 29001-1-29001-6
    • (2009) Europhys. Lett. , vol.86 , pp. 290011-290016
    • Constantin, A.1    Kartashova, E.2
  • 9
    • 32044450307 scopus 로고    scopus 로고
    • Variational formulations for steady water waves with vorticity
    • A. Constantin, D. Sattinger and W. Strauss, Variational formulations for steady water waves with vorticity, J. Fluid Mech., 548 (2006), 151-163.
    • (2006) J. Fluid Mech. , vol.548 , pp. 151-163
    • Constantin, A.1    Sattinger, D.2    Strauss, W.3
  • 10
    • 1242319077 scopus 로고    scopus 로고
    • Exact steady periodic water waves with vorticity
    • A. Constantin and W. Strauss, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57 (2004), 481-527.
    • (2004) Comm. Pure Appl. Math. , vol.57 , pp. 481-527
    • Constantin, A.1    Strauss, W.2
  • 11
    • 34247513994 scopus 로고    scopus 로고
    • Stability properties of steady water waves with vorticity
    • A. Constantin and W. Strauss, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., 60 (2007), 911-950.
    • (2007) Comm. Pure Appl. Math. , vol.60 , pp. 911-950
    • Constantin, A.1    Strauss, W.2
  • 13
    • 34547363845 scopus 로고    scopus 로고
    • Gravity surface wave turbulence in a laboratory flume
    • P. Denissenko, S. Lukaschuk and S. Nazarenko, Gravity surface wave turbulence in a laboratory flume, Phys. Rev. Lett., 99 (2007), 014501-1-014501-4
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 0145011-0145014
    • Denissenko, P.1    Lukaschuk, S.2    Nazarenko, S.3
  • 14
    • 58149212729 scopus 로고
    • Five-wave interaction on the surface of deep fluid
    • A. I. Dyachenko, Y. V. Lvov and V. E. Zakharov, Five-wave interaction on the surface of deep fluid, Physica D, 87 (1995), 233-261.
    • (1995) Physica D , vol.87 , pp. 233-261
    • Dyachenko, A.I.1    Lvov, Y.V.2    Zakharov, V.E.3
  • 15
    • 33847614874 scopus 로고    scopus 로고
    • Observation of gravity-capillary wave turbulence
    • E. Falcon, C. Laroche and S. Fauve, Observation of gravity-capillary wave turbulence, Phys. Rev. Lett., 98 (2007), 094503-1-094503-4
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 0945031-0945034
    • Falcon, E.1    Laroche, C.2    Fauve, S.3
  • 17
    • 0001979258 scopus 로고
    • Wave-current interactions
    • Wiley, New York
    • I. G. Jonsson, Wave-current interactions, in "The Sea," 65-120, Wiley, New York, 1990.
    • (1990) The Sea , pp. 65-120
    • Jonsson, I.G.1
  • 18
    • 0037564492 scopus 로고    scopus 로고
    • Experiments on deep water waves with two-dimensional surface patterns
    • J. L. Hammack and D. M. Henderson, Experiments on deep water waves with two-dimensional surface patterns, J. Offshore Mech. & Artic Eng., 125 (2003), 48-53.
    • (2003) J. Offshore Mech. & Artic Eng. , vol.125 , pp. 48-53
    • Hammack, J.L.1    Henderson, D.M.2
  • 19
    • 21344448402 scopus 로고    scopus 로고
    • Progressive waves with persistent, twodimensional surface patterns in deep water
    • J. L. Hammack, D. M. Henderson and H. Segur, Progressive waves with persistent, twodimensional surface patterns in deep water, J. Fluid Mech., 532 (2005), 1-51.
    • (2005) J. Fluid Mech. , vol.532 , pp. 1-51
    • Hammack, J.L.1    Henderson, D.M.2    Segur, H.3
  • 20
    • 84959594519 scopus 로고
    • A criterion for nonlinear wave stability
    • K. Hasselmann, A criterion for nonlinear wave stability, J. Fluid Mech., 30 (1967), 737-739.
    • (1967) J. Fluid Mech. , vol.30 , pp. 737-739
    • Hasselmann, K.1
  • 21
    • 0000832248 scopus 로고
    • Mathematical problems
    • D. Hubert, Mathematical problems, Bull. Amer. Math. Soc., 8 (1902), 437-479.
    • (1902) Bull. Amer. Math. Soc. , vol.8 , pp. 437-479
    • Hubert, D.1
  • 22
    • 33746350761 scopus 로고    scopus 로고
    • On the laboratory generation of twodimensional, progressive, surface waves of nearly permanent form on deep water
    • D. M. Henderson, M. S. Patterson and H. Segur, On the laboratory generation of twodimensional, progressive, surface waves of nearly permanent form on deep water, J. Fluid Mech., 559 (2006), 413-437.
    • (2006) J. Fluid Mech. , vol.559 , pp. 413-437
    • Henderson, D.M.1    Patterson, M.S.2    Segur, H.3
  • 23
    • 70350680731 scopus 로고
    • Resonant interactions of the water waves with discrete spectra
    • (ed. D.H. Peregrine), University of Bristol, UK
    • E. Kartashova, Resonant interactions of the water waves with discrete spectra, in "Proceedings of Nonlinear Water Waves Workshop" (ed. D.H. Peregrine), 43-53, University of Bristol, UK, 1992.
    • (1992) Proceedings of Nonlinear Water Waves Workshop , pp. 43-53
    • Kartashova, E.1
  • 24
    • 12044257588 scopus 로고
    • Weakly nonlinear theory of finite-size effects in resonators
    • E. Kartashova, Weakly nonlinear theory of finite-size effects in resonators, Phys. Rev. Lett., 72 (1994), 2013-2016.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 2013-2016
    • Kartashova, E.1
  • 25
    • 0002253566 scopus 로고    scopus 로고
    • Wave resonances in systems with discrete spectra
    • "Nonlinear Waves and Weak Turbulence" (ed. V.E. Zakharov)
    • E. Kartashova, Wave resonances in systems with discrete spectra, in "Nonlinear Waves and Weak Turbulence" (ed. V.E. Zakharov), AMS Trans. 2, 95-129, 1998.
    • (1998) AMS Trans. , vol.2 , pp. 95-129
    • Kartashova, E.1
  • 26
    • 33845762765 scopus 로고    scopus 로고
    • Fast computation algorithm for discrete resonances among gravity waves
    • E. Kartashova, Fast computation algorithm for discrete resonances among gravity waves, Low Temp. Phys., 145 (2006), 286-295.
    • (2006) Low Temp. Phys. , vol.145 , pp. 286-295
    • Kartashova, E.1
  • 27
    • 33745822473 scopus 로고    scopus 로고
    • A model of laminated turbulence
    • E. Kartashova, A model of laminated turbulence, JETP Lett., 83 (2006), 341-345.
    • (2006) JETP Lett. , vol.83 , pp. 341-345
    • Kartashova, E.1
  • 28
    • 34547318921 scopus 로고    scopus 로고
    • Exact and quasi-resonances in discrete water wave turbulence
    • E. Kartashova, Exact and quasi-resonances in discrete water wave turbulence, Phys. Rev. Lett., 98 (2007), 214502-1-214502-4
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 2145021-2145024
    • Kartashova, E.1
  • 29
    • 70350624978 scopus 로고    scopus 로고
    • Discrete wave turbulence
    • submitted. E-print: arXiv:0907.4406
    • E. Kartashova, Discrete wave turbulence, Europhys. Lett., submitted. E-print: arXiv:0907.4406
    • Europhys. Lett.
    • Kartashova, E.1
  • 30
    • 33845915566 scopus 로고    scopus 로고
    • Laminated wave turbulence: Generic algorithms I
    • E. Kartashova and A. Kartashov, Laminated wave turbulence: generic algorithms I, Int. J. Mod. Phys. C, 17 (2006), 1579-1596.
    • (2006) Int. J. Mod. Phys. C , vol.17 , pp. 1579-1596
    • Kartashova, E.1    Kartashov, A.2
  • 31
    • 34247895282 scopus 로고    scopus 로고
    • Laminated wave turbulence: Generic algorithms II
    • E. Kartashova and A. Kartashov, Laminated wave turbulence: generic algorithms II, Comm. Comp. Phys., 2 (2007), 783-794.
    • (2007) Comm. Comp. Phys. , vol.2 , pp. 783-794
    • Kartashova, E.1    Kartashov, A.2
  • 32
    • 34247866571 scopus 로고    scopus 로고
    • Laminated wave turbulence: Generic algorithms III
    • E. Kartashova and A. Kartashov, Laminated wave turbulence: generic algorithms III, Physics A: Stat. Mech. Appl., 380 (2007), 66-74.
    • (2007) Physics A: Stat. Mech. Appl. , vol.380 , pp. 66-74
    • Kartashova, E.1    Kartashov, A.2
  • 34
    • 62749118776 scopus 로고    scopus 로고
    • Cluster dynamics of planetary waves
    • E. Kartashova and V. S. L'vov, Cluster dynamics of planetary waves, Europhys. Lett., 83 (2008), 50012-1-50012-6
    • (2008) Europhys. Lett. , vol.83 , pp. 500121-500126
    • Kartashova, E.1    L'vov, V.S.2
  • 36
    • 47749151417 scopus 로고    scopus 로고
    • Resonant interactions of nonlinear water waves in a finite basin
    • E. Kartashova, S. Nazarenko and O. Rudenko, Resonant interactions of nonlinear water waves in a finite basin, Phys. Rev. E, 98 (2008), 0163041-1-0163041-9
    • (2008) Phys. Rev. E , vol.98 , pp. 01630411-01630419
    • Kartashova, E.1    Nazarenko, S.2    Rudenko, O.3
  • 37
    • 47749085259 scopus 로고    scopus 로고
    • Symbolic computations for nonlinear wave resonances
    • (ed. E. Pelinovsky and Ch. Kharif), Springer
    • E. Kartashova, C. Raab, Ch. Feurer, G. Mayrhofer and W. Schreiner, Symbolic computations for nonlinear wave resonances, in "Extreme Ocean Waves" (ed. E. Pelinovsky and Ch. Kharif), Springer, 97-128, 2008.
    • (2008) Extreme Ocean Waves , pp. 97-128
    • Kartashova, E.1    Raab, C.2    Feurer, Ch.3    Mayrhofer, G.4    Schreiner, W.5
  • 39
    • 68649111666 scopus 로고    scopus 로고
    • Renormalized resonance quartets in dispersive wave turbulence
    • W. Lee, G. Kovacic and D. Cai, Renormalized resonance quartets in dispersive wave turbulence, Phys. Rev. Lett., 103 (2009), 024502-1-024502-4
    • (2009) Phys. Rev. Lett. , vol.103 , pp. 0245021-0245024
    • Lee, W.1    Kovacic, G.2    Cai, D.3
  • 40
    • 33646898800 scopus 로고    scopus 로고
    • Discreteness and its effect on water-wave turbulence
    • Y. V. Lvov, S. Nazarenko and B. Pokorni, Discreteness and its effect on water-wave turbulence, Physica D, 218 (2006), 24-35.
    • (2006) Physica D , vol.218 , pp. 24-35
    • Lvov, Y.V.1    Nazarenko, S.2    Pokorni, B.3
  • 41
    • 0000528087 scopus 로고
    • The diophantineness of enumerable sets
    • Yu. Matijasevich, The diophantineness of enumerable sets, Soviet Math. Dokl, 11 (1970), 354-358.
    • (1970) Soviet Math. Dokl , vol.11 , pp. 354-358
    • Matijasevich, Yu.1
  • 42
    • 0000634221 scopus 로고
    • Resonant interactions among capillary-gravity waves
    • L. F. McGoldrick, Resonant interactions among capillary-gravity waves, J. Fluid Mech., 21 (1967), 305-331.
    • (1967) J. Fluid Mech. , vol.21 , pp. 305-331
    • McGoldrick, L.F.1
  • 45
    • 84974098014 scopus 로고
    • On the dynamics of unsteady gravity waves of infinite amplitude
    • O. M. Phillips, On the dynamics of unsteady gravity waves of infinite amplitude, J. Fluid Mech., 9 (1960), 193-217.
    • (1960) J. Fluid Mech. , vol.9 , pp. 193-217
    • Phillips, O.M.1
  • 46
    • 0345316029 scopus 로고
    • Theoretical and experimental studies of gravity wave interactions
    • O. M. Phillips, Theoretical and experimental studies of gravity wave interactions, Proc. Roy. Soc. Lond., A299 (1967), 104-119.
    • (1967) Proc. Roy. Soc. Lond. , vol.A299 , pp. 104-119
    • Phillips, O.M.1
  • 47
    • 0039164662 scopus 로고
    • Wave interactions
    • (eds. S. Leibovich and A.R. Seebass), Cornell University Press, Ithaca and London
    • O. M. Phillips, Wave interactions, in "Nonlinear Waves" (eds. S. Leibovich and A.R. Seebass), 186-205, Cornell University Press, Ithaca and London, 1974.
    • (1974) Nonlinear Waves , pp. 186-205
    • Phillips, O.M.1
  • 48
    • 0019562967 scopus 로고
    • Wave interactions - Evolution of an idea
    • O. M. Phillips, Wave interactions - evolution of an idea, J. Fluid Mech., 106 (1981), 215-227.
    • (1981) J. Fluid Mech. , vol.106 , pp. 215-227
    • Phillips, O.M.1
  • 49
    • 0033640486 scopus 로고    scopus 로고
    • Turbulence of capillary waves theory and numerical simulation
    • A. N. Pushkarev and V. E. Zakharov, Turbulence of capillary waves theory and numerical simulation, Physica D, 135 (2000), 98-116.
    • (2000) Physica D , vol.135 , pp. 98-116
    • Pushkarev, A.N.1    Zakharov, V.E.2
  • 50
    • 63049097754 scopus 로고    scopus 로고
    • Design of parametrically forced patterns and quasi-patterns
    • A. M. Rucklidge and M. Silber, Design of parametrically forced patterns and quasi-patterns, SIAM J. App. Dyn. Sys., 8 (2009), 298-347.
    • (2009) SIAM J. App. Dyn. Sys. , vol.8 , pp. 298-347
    • Rucklidge, A.M.1    Silber, M.2
  • 53
    • 0002128264 scopus 로고
    • Initial instability and long-time evolution of Stokes waves
    • (eds. Y. Toba, H. Mitsuyasu and F.D. Reidel), Dodrecht, Holland
    • L. Shemer and M. Stiassnie, Initial instability and long-time evolution of Stokes waves, in "The Ocean Surface" (eds. Y. Toba, H. Mitsuyasu and F.D. Reidel), 51-57, Dodrecht, Holland, 1985.
    • (1985) The Ocean Surface , pp. 51-57
    • Shemer, L.1    Stiassnie, M.2
  • 54
    • 14544290069 scopus 로고    scopus 로고
    • On the interactions of four water waves
    • M. Stiassnie and L. Shemer, On the interactions of four water waves, Wave motion, 41 (2005), 307-328.
    • (2005) Wave Motion , vol.41 , pp. 307-328
    • Stiassnie, M.1    Shemer, L.2
  • 55
    • 0035840904 scopus 로고    scopus 로고
    • Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations
    • M. Tanaka, Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations, J. Fluid Mech., 444 (2001), 199-221.
    • (2001) J. Fluid Mech. , vol.444 , pp. 199-221
    • Tanaka, M.1
  • 56
    • 34249006215 scopus 로고    scopus 로고
    • On the role of resonant interactions in the short-term evolution of deep-water ocean spectra
    • M. Tanaka, On the role of resonant interactions in the short-term evolution of deep-water ocean spectra, J. Phys. Oceanogr., 37 (2007), 1022-1036.
    • (2007) J. Phys. Oceanogr. , vol.37 , pp. 1022-1036
    • Tanaka, M.1
  • 57
    • 1242298969 scopus 로고    scopus 로고
    • Effects of discretization of the spectrum in water-wave turbulence
    • M. Tanaka and N. Yokoyama, Effects of discretization of the spectrum in water-wave turbulence, Fluid Dynamics Research, 34 (2004), 199-216.
    • (2004) Fluid Dynamics Research , vol.34 , pp. 199-216
    • Tanaka, M.1    Yokoyama, N.2
  • 58
    • 36149031567 scopus 로고
    • Proof of integrability for five-wave interactions in a case with unequal coupling constants
    • F. Verheest, Proof of integrability for five-wave interactions in a case with unequal coupling constants, J. Phys. A: Math. Gen., 21 (1988), L545-L549.
    • (1988) J. Phys. A: Math. Gen. , vol.21
    • Verheest, F.1
  • 59
    • 36549099986 scopus 로고
    • Integrability of restricted multiple three-wave interactions. II. Coupling constants with ratios 1 and S
    • F. Verheest, Integrability of restricted multiple three-wave interactions. II. Coupling constants with ratios 1 and S, J. Math. Phys., 29 (1988), 2197-2201.
    • (1988) J. Math. Phys. , vol.29 , pp. 2197-2201
    • Verheest, F.1
  • 60
    • 33947385856 scopus 로고    scopus 로고
    • A Hamiltonian formulation of water waves with constant vorticity
    • E. Wahlen, A Hamiltonian formulation of water waves with constant vorticity, Lett. Math. Phys., 79 (2007), 303-315.
    • (2007) Lett. Math. Phys. , vol.79 , pp. 303-315
    • Wahlen, E.1
  • 64
    • 0033133139 scopus 로고    scopus 로고
    • Statistical theory of gravity and capillary waves on the surface of a finitedepth fluid
    • V. E. Zakharov, Statistical theory of gravity and capillary waves on the surface of a finitedepth fluid, Eur. J. Mech. B: Fluids, (1999), 327-344.
    • (1999) Eur. J. Mech. B: Fluids , pp. 327-344
    • Zakharov, V.E.1
  • 68
    • 0040394181 scopus 로고
    • Integrability of nonlinear systems and perturbation theory
    • (ed. V.E. Zakharov), Springer
    • V. E. Zakharov and E. I. Shulman, Integrability of nonlinear systems and perturbation theory, in "What is Integrability?" (ed. V.E. Zakharov), Springer, 185-250, 1990.
    • (1990) What Is Integrability? , pp. 185-250
    • Zakharov, V.E.1    Shulman, E.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.