Автор |
Jones, M. C. W. |
Дата выпуска |
1995 |
dc.description |
The method of multiple scales, in both space and time, is used to derive a set of three nonlinear coupled partial differential equations which model the evolution of a train of capillary-gravity waves contained in a channel of finite depth and which arise from the resonant interaction of the Nth and (N + l)th harmonics of the fundamental mode. These equations are used to investigate the stability of the waves to plane-wave perturbations, which may be longitudinal, transverse or oblique to the direction of the propagation of the waves. |
Формат |
application.pdf |
Издатель |
Journals Oxford Ltd |
Копирайт |
Copyright Taylor and Francis Group, LLC |
Название |
Evolution equations which model the ripples arising from an adjacent mode interaction |
Тип |
research-article |
DOI |
10.1080/02681119508806201 |
Electronic ISSN |
1465-3389 |
Print ISSN |
0268-1110 |
Журнал |
Dynamics and Stability of Systems |
Том |
10 |
Первая страница |
163 |
Последняя страница |
178 |
Аффилиация |
Jones, M. C. W.; Department of Pure Mathematics, Queen's University |
Выпуск |
2 |
Библиографическая ссылка |
Benjamin, T. B and Feir, J. E. 1967. The disintegration of wavetrains on deep water. Part 1. Theory. Journal of Fluid Mechanics, 27: 417–430. |
Библиографическая ссылка |
Benney, D.J and Roskes, G.J. 1969. Wave instabilities. Studies in Applied Mathematics, 48: 377–385. |
Библиографическая ссылка |
Davey, A and Stewartson, K. 1974. On three dimensional packets of surface waves. Proceedings of the Royal Society of London A, 338: 101–110. |
Библиографическая ссылка |
Djordjevic, V. D and Redekopp, L. G. 1977. On two dimensional packets of capillary-gravity waves. Journal of Fluid Mechanics, 79: 703–714. |
Библиографическая ссылка |
Hasimoto, H and Ono, H. 1972. Nonlinear modulation of gravity waves. Journal of the Physical Society of Japan, 33: 805–811. |
Библиографическая ссылка |
Henderson, D. M and Hammack, J. L. 1987. Experiments on ripple instabilities, Part 1. Resonant triads. Journal ofFluid Mechanics, 184: 15–41. |
Библиографическая ссылка |
Jones, M. C. W. 1992. Nonlinear stability of resonant capillary-gravity waves. Wave Motion, 15: 267–283. |
Библиографическая ссылка |
Jones, M. C. W. 1993. On coupled differential equations which model the evolution of interacting capillary-gravity wave modes and related questions of stability. IMA Journal of Applied Mathematics, 50: 13–28. |
Библиографическая ссылка |
McGoldrick, L. F. 1970. On Wilton's ripples: a special case of resonant interactions. Journal of Fluid Mechanics, 42: 193–200. |
Библиографическая ссылка |
McGoldrick, L. F. 1972. On the rippling of small waves: a harmonic nonlinear nearly resonant interaction. Journal of Fluid Mechanics, 52: 725–751. |
Библиографическая ссылка |
Nayfeh, A. H. 1970a. Finite amplitude surface waves in a liquid layer. Journal of Fluid Mechanics, 40: 671–684. |
Библиографическая ссылка |
Nayfeh, A. H. 1970b. Triple- and quintuple-dimpled wave profiles in deep water. Physics of Fluids, 13: 545–550. |
Библиографическая ссылка |
Nayfeh, A. H. 1971. Journal of Fluid Mechanics, 48: 384–395. |
Библиографическая ссылка |
Nayfeh, A. H. 1973. Second harmonic resonance in the interaction of an air stream with capillary- gravity waves. Journal of Fluid Mechanics, 59: 803–816. |
Библиографическая ссылка |
Perlin, M and Hammack, J. 1991. Experiments on ripple instabilities. Part 3. Resonant quartets of the Benjamin-Feir type. Journal of Fluid Mechanics, 229: 229–268. |
Библиографическая ссылка |
Zakharov, V. E. 1968. Stability of periodic waves of finite amplitude on the surface of a deep fluid. Journal of Applied Mechanics and Technical Physics, 2: 190–194. |
Библиографическая ссылка |
Zhang, J and Melville, W. K. 1987. Three dimensional instabilities of nonlinear gravity-capillary waves. Journal of Fluid Mechanics, 174: 187–208. |