메뉴 건너뛰기




Volumn 79, Issue 3, 2007, Pages 303-315

A Hamiltonian formulation of water waves with constant vorticity

Author keywords

Constant vorticity; Hamiltonian formulation; Water waves

Indexed keywords


EID: 33947385856     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-007-0143-5     Document Type: Article
Times cited : (75)

References (32)
  • 1
    • 0020292888 scopus 로고
    • Hamiltonian structures, symmetries and conservation laws for water waves
    • Benjamin, T.B., Olver, P.J.: Hamiltonian structures, symmetries and conservation laws for water waves. J. Fluid Mech. 125, 137-185 (1982)
    • (1982) J. Fluid Mech , vol.125 , pp. 137-185
    • Benjamin, T.B.1    Olver, P.J.2
  • 2
    • 3142676320 scopus 로고    scopus 로고
    • Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation
    • Buffoni, B.: Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation. Arch. Ration. Mech. Anal. 173, 25-68 (2004)
    • (2004) Arch. Ration. Mech. Anal , vol.173 , pp. 25-68
    • Buffoni, B.1
  • 3
    • 33947385263 scopus 로고    scopus 로고
    • Conditional energetic stability of gravity solitary waves in the presence of weak surface tension
    • Buffoni, B.: Conditional energetic stability of gravity solitary waves in the presence of weak surface tension. Topol. Methods Nonlinear Anal. 25, 41-68 (2005)
    • (2005) Topol. Methods Nonlinear Anal , vol.25 , pp. 41-68
    • Buffoni, B.1
  • 4
    • 0039896325 scopus 로고    scopus 로고
    • On the deep water wave motion
    • Constantin, A.: On the deep water wave motion. J. Phys. A 34, 1405-1417 (2001)
    • (2001) J. Phys. A , vol.34 , pp. 1405-1417
    • Constantin, A.1
  • 5
    • 33947415186 scopus 로고    scopus 로고
    • Constantin, A.: Wave-current interactions. In: EQUADIFF 2003, pp. 207-212. World Scientific, Hackensak, N.T (2005)
    • Constantin, A.: Wave-current interactions. In: EQUADIFF 2003, pp. 207-212. World Scientific, Hackensak, N.T (2005)
  • 6
    • 30444435970 scopus 로고    scopus 로고
    • A Hamiltonian formulation for free surface water waves with non-vanishing vorticity
    • Constantin, A.: A Hamiltonian formulation for free surface water waves with non-vanishing vorticity. J. Nonl. Math. Phys. 12, 202-211 (2005)
    • (2005) J. Nonl. Math. Phys , vol.12 , pp. 202-211
    • Constantin, A.1
  • 7
    • 33750526877 scopus 로고    scopus 로고
    • The trajectories of particles in Stokes waves
    • Constantin, A.: The trajectories of particles in Stokes waves. Invent. Math. 166, 523-535 (2006)
    • (2006) Invent. Math , vol.166 , pp. 523-535
    • Constantin, A.1
  • 8
    • 1242299759 scopus 로고    scopus 로고
    • Symmetry of steady periodic surface water waves with vorticity
    • Constantin, A., Escher, J.: Symmetry of steady periodic surface water waves with vorticity. J. Fluid Mech. 498, 171-181 (2004)
    • (2004) J. Fluid Mech , vol.498 , pp. 171-181
    • Constantin, A.1    Escher, J.2
  • 9
    • 17044390729 scopus 로고    scopus 로고
    • Symmetry of steady deep-water waves with vorticity
    • Constantin, A., Escher, J.: Symmetry of steady deep-water waves with vorticity. Eur. J. Appl. Math. 15, 755-768 (2004)
    • (2004) Eur. J. Appl. Math , vol.15 , pp. 755-768
    • Constantin, A.1    Escher, J.2
  • 10
    • 44949249867 scopus 로고    scopus 로고
    • Nearly-Hamiltonian structure for water waves with constant vorticity
    • to appear
    • Constantin, A., Ivanov, R.I., Prodanov, E.M.: Nearly-Hamiltonian structure for water waves with constant vorticity. J. Math. Fluid Mech. (to appear)
    • J. Math. Fluid Mech
    • Constantin, A.1    Ivanov, R.I.2    Prodanov, E.M.3
  • 11
    • 1242319077 scopus 로고    scopus 로고
    • Exact steady periodic water waves with vorticity
    • Constantin, A., Strauss, W.: Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math. 57, 481-527 (2004)
    • (2004) Comm. Pure Appl. Math , vol.57 , pp. 481-527
    • Constantin, A.1    Strauss, W.2
  • 12
    • 32044450307 scopus 로고    scopus 로고
    • Variational formulations for steady water waves with vorticity
    • Constantin, A., Sattinger, D.H., Strauss, W.: Variational formulations for steady water waves with vorticity. J. Fluid Mech. 548, 151-163 (2006)
    • (2006) J. Fluid Mech , vol.548 , pp. 151-163
    • Constantin, A.1    Sattinger, D.H.2    Strauss, W.3
  • 13
    • 33947400911 scopus 로고    scopus 로고
    • Craig, W.: Water waves, Hamiltonian systems and Cauchy integrals. In: Microlocal Analysis and Nonlinear Waves (Minneapolis, MN, 1988-1989), pp. 37-45, IMA Mathematical Applications, 30. Springer, New York (1991)
    • Craig, W.: Water waves, Hamiltonian systems and Cauchy integrals. In: Microlocal Analysis and Nonlinear Waves (Minneapolis, MN, 1988-1989), pp. 37-45, IMA Volume Mathematical Applications, 30. Springer, New York (1991)
  • 14
    • 0028443419 scopus 로고
    • Hamiltonian long-wave approximations to the water-wave problem
    • Craig, W., Groves, M.: Hamiltonian long-wave approximations to the water-wave problem. Wave Motion 19, 367-389 (1994)
    • (1994) Wave Motion , vol.19 , pp. 367-389
    • Craig, W.1    Groves, M.2
  • 15
    • 33747159045 scopus 로고    scopus 로고
    • Uniqueness for steady water waves with vorticity
    • Ehrnström, M.: Uniqueness for steady water waves with vorticity. Int. Math. Res. Not. 2005, 3721-3726 (2005)
    • (2005) Int. Math. Res. Not , vol.2005 , pp. 3721-3726
    • Ehrnström, M.1
  • 16
    • 77952870940 scopus 로고
    • Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile
    • Gerstner, F.: Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile. Ann. Phys. 2, 412-445 (1809)
    • (1809) Ann. Phys , vol.2 , pp. 412-445
    • Gerstner, F.1
  • 17
    • 0036110969 scopus 로고    scopus 로고
    • Finite-wavelength stability of capillary-gravity solitary waves
    • Haragus, M., Scheel, A.: Finite-wavelength stability of capillary-gravity solitary waves. Comm. Math. Phys. 225, 487-521 (2002)
    • (2002) Comm. Math. Phys , vol.225 , pp. 487-521
    • Haragus, M.1    Scheel, A.2
  • 18
    • 33947391591 scopus 로고    scopus 로고
    • Variational principles for water waves
    • Kolev, B., Sattinger, D.H.: Variational principles for water waves. SIAM J. Math. Anal. 38, 906-920 (2006)
    • (2006) SIAM J. Math. Anal , vol.38 , pp. 906-920
    • Kolev, B.1    Sattinger, D.H.2
  • 19
    • 0000454190 scopus 로고
    • The Hamiltonian structure for dynamic free boundary problems
    • Lewis, D., Marsden, J., Montgomery, R., Ratiu, T.: The Hamiltonian structure for dynamic free boundary problems. Physica D 18, 391-404 (1986)
    • (1986) Physica D , vol.18 , pp. 391-404
    • Lewis, D.1    Marsden, J.2    Montgomery, R.3    Ratiu, T.4
  • 20
    • 0017889140 scopus 로고
    • Cambridge University Press, Cambridge
    • Lighthill, J.: Waves in Fluids. Cambridge University Press, Cambridge (1978)
    • (1978) Waves in Fluids
    • Lighthill, J.1
  • 21
    • 84974513241 scopus 로고
    • A variational principle for a fluid with a free surface
    • Luke, J.C.: A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395-397 (1967)
    • (1967) J. Fluid Mech , vol.27 , pp. 395-397
    • Luke, J.C.1
  • 22
    • 21844498358 scopus 로고
    • An unconstrained Hamiltonian formulation for incompressible fluid flow
    • Maddocks, J.H., Pego, R.L.: An unconstrained Hamiltonian formulation for incompressible fluid flow. Comm. Math. Phys. 170, 207-217 (1995)
    • (1995) Comm. Math. Phys , vol.170 , pp. 207-217
    • Maddocks, J.H.1    Pego, R.L.2
  • 23
    • 0037107586 scopus 로고    scopus 로고
    • Mielke, A.: On the energetic stability of solitary water waves. Phil. Trans. R. Soc. Loud. A 360, 2337-2358 (2002)
    • Mielke, A.: On the energetic stability of solitary water waves. Phil. Trans. R. Soc. Loud. A 360, 2337-2358 (2002)
  • 24
    • 84974055944 scopus 로고
    • A note regarding 'On Hamilton's principle for water waves'
    • Milder, D.M.: A note regarding 'On Hamilton's principle for water waves'. J. Fluid Mech. 83, 159-161 (1977)
    • (1977) J. Fluid Mech , vol.83 , pp. 159-161
    • Milder, D.M.1
  • 25
    • 84974144443 scopus 로고
    • On Hamilton's principle for water waves
    • Miles, J.W.: On Hamilton's principle for water waves. J. Fluid Mech. 83, 153-158 (1977)
    • (1977) J. Fluid Mech , vol.83 , pp. 153-158
    • Miles, J.W.1
  • 27
    • 0035065679 scopus 로고    scopus 로고
    • An experimental study of two-dimensional surface water waves propagating on depth-varying currents
    • Swan, C., Cummins, I.P., James, R.L.: An experimental study of two-dimensional surface water waves propagating on depth-varying currents. J. Fluid Mech. 428, 273-304 (2001)
    • (2001) J. Fluid Mech , vol.428 , pp. 273-304
    • Swan, C.1    Cummins, I.P.2    James, R.L.3
  • 28
    • 84972192041 scopus 로고
    • Steep, steady surface waves on water of finite depth with constant vorticity
    • Teles da Silva, A.F., Peregrine, D.H.: Steep, steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281-302 (1988)
    • (1988) J. Fluid Mech , vol.195 , pp. 281-302
    • Teles da Silva, A.F.1    Peregrine, D.H.2
  • 29
    • 0001016510 scopus 로고    scopus 로고
    • Wave-current interactions in the nearshore region
    • Southampton, United Kingdom
    • Thomas, G., Klopman, G.: Wave-current interactions in the nearshore region, in Gravity waves in water of finite depth, pp. 215-319. Southampton, United Kingdom, (1997)
    • (1997) Gravity waves in water of finite depth , pp. 215-319
    • Thomas, G.1    Klopman, G.2
  • 30
    • 33947164511 scopus 로고    scopus 로고
    • Steady periodic capillary waves with vorticity
    • to appear
    • Wahlén, E.: Steady periodic capillary waves with vorticity. Ark. Mat. (to appear)
    • Ark. Mat
    • Wahlén, E.1
  • 31
    • 33947375479 scopus 로고    scopus 로고
    • Steady periodic capillary-gravity waves with vorticity
    • Wahlén, E.: Steady periodic capillary-gravity waves with vorticity. SIAM J. Math. Anal. 38, 921-943 (2006)
    • (2006) SIAM J. Math. Anal , vol.38 , pp. 921-943
    • Wahlén, E.1
  • 32
    • 0001834355 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of a deep fluid
    • Zakharov, V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. Zh. Prikl. Mekh. Tekh. Fiz. 9, 86-94 (1968)
    • (1968) Zh. Prikl. Mekh. Tekh. Fiz , vol.9 , pp. 86-94
    • Zakharov, V.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.