메뉴 건너뛰기




Volumn 10, Issue 2, 2008, Pages 224-237

Nearly-Hamiltonian structure for water waves with constant vorticity

Author keywords

Constant vorticity; Hamiltonian formulation; Water waves

Indexed keywords

HAMILTONIANS; NUMERICAL METHODS; VORTICITY;

EID: 44949249867     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-006-0230-x     Document Type: Article
Times cited : (54)

References (33)
  • 1
    • 0000542179 scopus 로고
    • On periodic water-waves and their convergence to solitary waves in the long-wave limit
    • C. J. AMICK and J. F. TOLAND, On periodic water-waves and their convergence to solitary waves in the long-wave limit, Philos. Trans. Roy. Soc. London Ser. A 303 (1981), 633-669.
    • (1981) Philos. Trans. Roy. Soc. London Ser. A , vol.303 , pp. 633-669
    • AMICK, C.J.1    TOLAND, J.F.2
  • 2
    • 0020292888 scopus 로고
    • Hamiltonian structure, symmetries and conservation laws for water waves
    • T. B. BENJAMIN and P. J. OLVER, Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.
    • (1982) J. Fluid Mech , vol.125 , pp. 137-185
    • BENJAMIN, T.B.1    OLVER, P.J.2
  • 4
    • 0036341189 scopus 로고    scopus 로고
    • Vector calculus and the topology of domains in 3-space
    • J. CANTARELLA, D. DETURCK and H. GLUCK, Vector calculus and the topology of domains in 3-space, Amer. Math. Monthly 109 (2002), 409-442.
    • (2002) Amer. Math. Monthly , vol.109 , pp. 409-442
    • CANTARELLA, J.1    DETURCK, D.2    GLUCK, H.3
  • 5
    • 0039896325 scopus 로고    scopus 로고
    • On the deep water wave motion
    • A. CONSTANTIN, On the deep water wave motion, J. Phys. A 34 (2001), 1405-1417.
    • (2001) J. Phys. A , vol.34 , pp. 1405-1417
    • CONSTANTIN, A.1
  • 6
    • 0035900644 scopus 로고    scopus 로고
    • Edge waves along a sloping beach
    • A. CONSTANTIN, Edge waves along a sloping beach, J. Phys. A 34 (2001), 9723-9731.
    • (2001) J. Phys. A , vol.34 , pp. 9723-9731
    • CONSTANTIN, A.1
  • 7
    • 30444435970 scopus 로고    scopus 로고
    • A Hamiltonian formulation for free surface water waves with non-vanishing vorticity
    • A. CONSTANTIN, A Hamiltonian formulation for free surface water waves with non-vanishing vorticity, J. Nonl. Math. Phys. 12 (2005), 202-211.
    • (2005) J. Nonl. Math. Phys , vol.12 , pp. 202-211
    • CONSTANTIN, A.1
  • 8
    • 44949083255 scopus 로고    scopus 로고
    • Wave-current interactions
    • World Sci. Publ, Hackensack, NJ
    • A. CONSTANTIN, Wave-current interactions, in: EQUADIFF 2003, 207-212, World Sci. Publ., Hackensack, NJ, 2005.
    • (2005) EQUADIFF 2003 , pp. 207-212
    • CONSTANTIN, A.1
  • 9
    • 33750526877 scopus 로고    scopus 로고
    • The trajectories of particles in Stokes waves
    • A. CONSTANTIN, The trajectories of particles in Stokes waves, Invent. Math. 166 (2006), 523-535.
    • (2006) Invent. Math , vol.166 , pp. 523-535
    • CONSTANTIN, A.1
  • 10
    • 1242299759 scopus 로고    scopus 로고
    • Symmetry of steady periodic surface water waves with vorticity
    • A. CONSTANTIN and J. ESCHER, Symmetry of steady periodic surface water waves with vorticity, J. Fluid Mech. 498 (2004), 171-181.
    • (2004) J. Fluid Mech , vol.498 , pp. 171-181
    • CONSTANTIN, A.1    ESCHER, J.2
  • 11
    • 0038391364 scopus 로고    scopus 로고
    • Exact periodic traveling water waves with vorticity
    • A. CONSTANTIN and W. STRAUSS, Exact periodic traveling water waves with vorticity, C. R. Math. Acad. Sci. Paris 335 (2002), 797-800.
    • (2002) C. R. Math. Acad. Sci. Paris , vol.335 , pp. 797-800
    • CONSTANTIN, A.1    STRAUSS, W.2
  • 12
    • 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
  • 13
    • 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
  • 14
    • 34247513994 scopus 로고    scopus 로고
    • Stability properties of steady water waves with vorticity
    • in print
    • A. CONSTANTIN and W. STRAUSS, Stability properties of steady water waves with vorticity, Comm. Pure Appl. Math., in print.
    • Comm. Pure Appl. Math
    • CONSTANTIN, A.1    STRAUSS, W.2
  • 15
    • 30444438571 scopus 로고
    • Water waves, Hamiltonian systems and Cauchy integrals
    • Minneapolis, MN
    • W. CRAIG, Water waves, Hamiltonian systems and Cauchy integrals, in: Microlocal Analysis and Nonlinear Waves (Minneapolis, MN, 1988-1989), 37-45
    • (1988) Microlocal Analysis and Nonlinear Waves , pp. 37-45
    • CRAIG, W.1
  • 16
    • 44949226726 scopus 로고
    • Appl, 30, Springer, New York
    • IMA Vol. Math. Appl., 30, Springer, New York, 1991.
    • (1991)
    • Vol, I.M.A.1    Math2
  • 17
    • 0028443419 scopus 로고
    • Hamiltonian long-wave approximations to the water-wave problem
    • W. CRAIG and M. D. GROVES, Hamiltonian long-wave approximations to the water-wave problem, Wave Motion 19 (1994), 367-389.
    • (1994) Wave Motion , vol.19 , pp. 367-389
    • CRAIG, W.1    GROVES, M.D.2
  • 18
    • 84972192041 scopus 로고
    • Steep, steady surface waves on water of finite depth with constant vorticity
    • A. F. T. DASILVA and D. H. PEREGRINE, Steep, steady surface waves on water of finite depth with constant vorticity, J. Fluid Mech. 195 (1988), 281-302.
    • (1988) J. Fluid Mech , vol.195 , pp. 281-302
    • DASILVA, A.F.T.1    PEREGRINE, D.H.2
  • 19
    • 33747159045 scopus 로고    scopus 로고
    • Uniqueness for steady water waves with vorticity
    • M. EHRNSTRÖM, Uniqueness for steady water waves with vorticity, Int. Math. Res. Not. 60 (2005), 3721-3726.
    • (2005) Int. Math. Res. Not , vol.60 , pp. 3721-3726
    • EHRNSTRÖM, M.1
  • 20
    • 77952870940 scopus 로고
    • Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile
    • F. GERSTNER, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile, Ann. Phys. 2 (1809), 412-445.
    • (1809) Ann. Phys , vol.2 , pp. 412-445
    • GERSTNER, F.1
  • 21
    • 0031375381 scopus 로고    scopus 로고
    • On variational formulations for steady water waves
    • M. D. GROVES and J. F. TOLAND, On variational formulations for steady water waves, Arch. Rat. Mech. Anal. 137 (1997), 203-226.
    • (1997) Arch. Rat. Mech. Anal , vol.137 , pp. 203-226
    • GROVES, M.D.1    TOLAND, J.F.2
  • 23
    • 33947391591 scopus 로고    scopus 로고
    • Variational principles for stationary waves
    • B. KOLEV and D. H. SATTINGER, Variational principles for stationary waves, SIAM J. Math. Anal. 38 (2006), 906-920.
    • (2006) SIAM J. Math. Anal , vol.38 , pp. 906-920
    • KOLEV, B.1    SATTINGER, D.H.2
  • 24
    • 0017889140 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • J. LIGHTHILL, Waves in Fluids, Cambridge Univ. Press, Cambridge, 1978.
    • (1978) Waves in Fluids
    • LIGHTHILL, J.1
  • 27
    • 0000025473 scopus 로고
    • On the theory of oscillatory waves
    • G. STOKES, On the theory of oscillatory waves, Trans. Cambridge Phil. Soc. 8 (1847), 441-455.
    • (1847) Trans. Cambridge Phil. Soc , vol.8 , pp. 441-455
    • STOKES, G.1
  • 28
    • 0035065679 scopus 로고    scopus 로고
    • C. SWAN, I. CUMMINSand R. JAMES, An experimental study of two-dimensional surface water waves propagating on depth-varying currents, J. Fluid Mech. 428 (2001), 273-304.
    • C. SWAN, I. CUMMINSand R. JAMES, An experimental study of two-dimensional surface water waves propagating on depth-varying currents, J. Fluid Mech. 428 (2001), 273-304.
  • 29
    • 0025458965 scopus 로고
    • Wave-current interactions: An experimental and numerical study
    • G. THOMAS, Wave-current interactions: an experimental and numerical study, J. Fluid Mech. 216 (1990), 505-536.
    • (1990) J. Fluid Mech , vol.216 , pp. 505-536
    • THOMAS, G.1
  • 31
    • 16244386572 scopus 로고    scopus 로고
    • A note on steady gravity waves with vorticity
    • E. WAHLEN, A note on steady gravity waves with vorticity, Int. Math. Res. Not. 7 (2005), 389-396.
    • (2005) Int. Math. Res. Not , vol.7 , pp. 389-396
    • WAHLEN, E.1
  • 33
    • 34250447917 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of a deep fluid
    • V. E. ZAKHAROV, Stability of periodic waves of finite amplitude on the surface of a deep fluid, J. Appl. Mech. Tech. Phys. 2 (1968), 190-194.
    • (1968) J. Appl. Mech. Tech. Phys , vol.2 , pp. 190-194
    • ZAKHAROV, V.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.