The current-modified nonlinear Schrödinger equation

Journal of Fluid Mechanics

Volumn 399, Issue , 1999, Pages 335-353

  Stocker, J R ^a   Peregrine, D H ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 6044269428     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099006618     Document Type: Article

References (29)

1. ABLOWITZ, M. J. & HERBST, B. M. 1990 On the homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. SIAM J. Appl. Maths 50, 339-351.
2. BAKHANOV, V. V., BOGATYREV, S. D., KAZAKOV, V. I. et al. 1997 Laboratory investigations of nonlinear surface wave transformation in a field of two-dimensionally inhomogeneous currents. Intl. Geoscience & Remote Sensing Sympos. Proc. I, 350-352.
3. BAKHANOV, V. V., KEMARSKAYA, O. N., POZDNYAKOVA, V. I. et al. 1996 Evolution of surface waves of finite amplitude in field of inhomogeneous current. Intl. Geoscience & Remote Sensing Sympos. Proc. I, 609-611.
4. BRETHERTON, F. P. & GARRETT, C. J. R. 1968 Wavetrains in inhomogeneous moving media. Proc. R. Soc. Lond. A 302, 529-554.
5. BRINCH-NIELSEN, U. 1985 Slowly modulated, weakly nonlinear gravity waves-fourth order evolution equations and stability analysis. MSc thesis, Tech. Univ. Denmark, pp. 99-109.
6. DAVEY, A. & STEWARTSON, K. 1974 On three-dimensional packets of surface waves. Proc. R. Soc. Lond. A 338, 101-110.
7. DHAR, A. K. & DAS, K. P. 1994 Stability analysis from fourth order evolution equation for small but finite amplitude interfacial waves in the presence of a basic current shear. J. Austral. Math. Soc. B 35, 348-365.
8. DOLD, J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103, 90-115.
9. DOLD, J. W. & PEREGRINE, D. H. 1986 An efficient boundary-integral method for steep unsteady water waves. In Numerical Methods for Fluid Dynamics II (ed. K. W. Morton & M. J. Baines), pp. 671-679. Oxford University Press.
10. DONATO, A. N., PEREGRINE, D. H. & STOCKER, J. R. 1999 The focussing of surface waves by internal waves. J. Fluid Mech. 384, 27-58 (referred to herein as DPS).
11. DYSTHE, K. B. 1979 Note on the modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105-114.
12. GARGETT, A. E. & HUGHES, B. A. 1972 On the interaction of surface and internal waves. J. Fluid Mech. 52, 179-191.
13. HASIMOTO, H. & ONO, H. 1972 Nonlinear modulation of gravity waves. J. Phys. Soc. Japan. 33, 805-811.
14. JONSSON, J. J. 1990 Wave-current interactions. In The Sea (ed. B. le Mehaute & D. M. Haine), pp. 65-120. Wiley-Interscience.
15. LAMB, H. 1932 Hydrodynamics, 6th Edn, Chap. IX, pp. 417-420. Cambridge University Press.
16. Lo, E. & MEI, C. C. 1985 Numerical study of water-wave modulation. J. Fluid Mech. 150, 395-415.
17. LONGUET-HIGGINS, M. S. & STEWARD R. W. 1964 Radiation stress in water waves, a physical discussion with application. Deep-Sea Res. 11, 529-562.
18. PEREGRINE, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9-117.
19. PULLIN, D. I. & GRIMSHAW, R. H. J. 1986 Stability of finite amplitude interfacial waves. Part 3. The effect of a basic current shear for one dimensional instabilities. J. Fluid Mech. 172, 277-306.
20. SCHWARTZ, L. W. 1973 Computer extension and analytic continuation of Stokes expansion for gravity waves. J. Fluid Mech. 62, 553-578.
21. TANAKA, M. 1983 The stability of steep gravity waves. J. Phys. Soc. Japan 52, 3047-3055.
22. TRULSEN, K. & DYSTHE, K. B. 1996 A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281-289.
23. TRULSEN, K. & DYSTHE, K. B. 1997 Frequency downshift in three-dimensional wave trains. J. Fluid Mech. 352, 359-373.
24. TRULSEN, K., STANSBERG, C. T. & VELARDE, M. G. 1999 Laboratory evidence of three-dimensional frequency downshift of waves in a long tank. Phys. Fluids 11, No.1.
25. WEIDMAN, J. A. C. & HERBST, B. M. 1986 Split-step methods for the solution of the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 23, 485-507.
26. WHITHAM, G. B. 1965 A general approach to linear and non-linear dispersive waves using a Lagrangian. J. Fluid Mech. 22, 273-283.
27. WHITHAM, G. B. 1967 Non-linear dispersion of water waves. J. Fluid Mech. 27, 399-412.
28. YUEN, H. C. & LAKE, B. M. 1982 Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech. 22, 67-229.
29. ZAKHAROV, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep water fluid. J. Appl. Mech. Tech. Phys. (Engl. Transl.) 2, 190-194.