A method for computing unsteady fully nonlinear interfacial waves

Journal of Fluid Mechanics

Volumn 351, Issue , 1997, Pages 223-252

  Grue, John ^a   Friis, Helmer André ^a   Palm, Enok ^a   Rusås, Per Olav ^a  

^a UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

CAUCHY THEOREM; INTERFACIAL WAVES;

UNSTEADY FLOW;

EID: 0031274219     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112097007428     Document Type: Article

References (38)

1. AMICK, C. J. & TURNER, R. E. L. 1986 A global theory of internal solitary waves in two-fluid systems. Trans. Am. Math. Soc. 298, 431.
2. APEL, J. R., HOLBROOK, J. R., LIU, A. K. & TSAI, J. 1985 The Sulu Sea internal soliton experiment. J. Phys. Oceanogr. 15, 1625.
3. BAINES, P. 1984 A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127.
4. BAKER, G. R., MEIRON, D. I. & ORSZAG, S. A. 1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477.
5. BENJAMIN, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559.
6. CASCIOLA, C. M. & LANDRINI, M. 1996 Nonlinear long waves generated by a moving pressure disturbance. J. Fluid Mech. 325, 399.
7. DAVIS, R. E. & ACRIVOS, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29, 593.
8. DOLD, J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves J. Comput. Phys. 103, 90.
9. DOLD, J. W. & PEREGRINE, D. H. 1985 An efficient boundary-integral equation method for steep unsteady water waves. In Numerical Methods for Fluid Dynamics, vol. 2 (ed. K. W. Morton & M. J. Baines), Clarenden, pp. 671-679.
10. ELIASSEN, A. 1982 Vilhelm Bjerknes and his students. Ann. Rev. Fluid Mech. 14, 1.
11. ELIASSEN, A. & FJØRTOFT, R. 1992 The interface method for calculating the temporal evolution of a two-fluid system. Frontiers of Science, Ann. NY Acad. Sci. 661, 54.
12. FARMER, D. M. & SMITH, J. D. 1980 Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res. 27A, 239.
13. FRIIS, H. A. 1995 On nonlinear free surface and interfacial water waves and their interaction with submerged bodies. Dr. Scient. Thesis, Dept. of Mathematics, The University of Oslo.
14. GRIMSHAW, R. H. J. & SMYTH, N. 1986 Resonant flow of a stratified fluid over topography. J. Fluid Mech. 169, 429.
15. HOLYER, J. Y. 1979 Large amplitude progressive interfacial waves. J. Fluid Mech. 93, 433.
16. JOSEPH, R. I. 1977 Solitary waves in a finite depth fluid. J. Phys. A: Math. Gen. 10, L225.
17. KEULEGAN, G. H. 1953 Characteristics of internal solitary waves. J. Res. Natl Bur. Stand. 51, 133.
18. KOOP, C. G. & BUTLER, G. 1981 An investigation on internal solitary waves in a two-fluid system. J. Fluid Mech. 112, 225.
19. KUBOTA, T., KO, D. R. S. & DOBBS, L. D. 1978 Weakly-nonlinear, long internal gravity waves in stratified fluids of finite depth. J. Hydronaut. 12, 157.
20. LONG, R. R. 1956 Solitary waves in one and two fluid systems. Tellus 8, 460.
21. MEIRON, D. I. & SAFEMAN, P. G. 1983 Overhanging interfacial garvity waves of large amplitude. J. Fluid Mech. 120, 213.
22. MELVILLE, W. K. & HELFRICH, K. R. 1987 Transcritical two-layer flow over topography. J. Fluid Mech. 178, 31 (referred to herein as MH).
23. MILES, J. W. 1979 On internal solitary waves. Tellus 31, 456.
24. MILES, J. W. 1981 On internal solitary waves II. Tellus 33, 397.
25. ONO, H. 1975 Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan 39, 1082.
26. PULLIN, D. I. & GRIMSHAW, R. H. J. 1988 Finite-amplitude solitary waves at the interface between two homogeneous fluids. Phys. Fluids 31, 3550.
27. ROBERTS, A. J. 1983 A stable and accurate numerical method to calculate the motion of a sharp interface between fluids. IMA J. Appl. Math. 31, 31.
28. SCHULTZ, W. W., HUH, J. & GRIEFIN, O. M. 1994 Potential energy in steep and breaking waves. J. Fluid Mech. 278, 201.
29. SEGUR, H. & HAMMACK, J. L. 1982 Soliton models of long internal waves. J. Fluid Mech. 118, 285.
30. SHELLEY, M. J. 1992 A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method. J. Fluid Mech. 244, 493.
31. STAQUET, C. & SOMMERIA, J. 1996 Internal waves, turbulence and mixing in stratified flows: a report on Euromech Colloquium 339. J. Fluid Mech. 314, 349.
32. TURNER, R. E. L. & VANDEN-BROECK, J.-M. 1986 The limiting configuration of interfacial gravity waves. Phys. Fluids 29, 372.
33. TURNER, R. E. L. & VANDEN-BROFCK, J.-M. 1988 Broadening of interfacial solitary waves. Phys. Fluids 31, 2486.
34. VANDEN-BROECK, J.-M. 1980 Numerical calculation of gravity-capillary interfacial waves of finite amplitude. Phys. Fluids 23, 1723.
35. VINJE, T. & BREVIG, P. 1981 Numerical simulation of breaking waves. Adv. Water Res. 4, 77.
36. WU, T. Y. 1987 Generation of upstream advancing solitons by moving disturbances. J. Fluid Mech. 184, 75.
37. ZHOU, Q.-N. & GRAEBEL, W. P. 1990 Axisymmetric draining of a cylindrical tank with a free surface. J. Fluid Mech. 221, 511.
38. ZHU, J., WU, T. Y. & YATES, G. T. 1987 Internal solitary waves generated by moving disturbances. 3rd Intl Symp. on Stratified Flows, California Inst. of Tech., Pasadena, California, 3-5 February, p. 1