Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-21T22:46:45.578Z Has data issue: false hasContentIssue false
  • English
  • Français

Theory of weakly damped Stokes waves: a new formulation and its physical interpretation

Published online by Cambridge University Press:  26 April 2006

Michael S. Longuet-Higgins
Michael S. Longuet-Higgins
Affiliation:
Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A tractable theory for weakly damped, nonlinear Stokes waves on deep water was recently formulated by Ruvinsky & Friedman (1985a, b; 1987). In this paper we show how the theory can be simplified, and that it is equivalent to a boundary-layer model for surface waves proposed by Longuet-Higgins (1969), when the latter is generalized to include surface tension and nonlinearity. The potential part of the flow is determined by boundary conditions applied at the base of the vortical boundary layer. The theory may be of use in discussing the generation of waves by wind.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 235 , February 1992 , pp. 319 - 324
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535–581.Google Scholar
Longuet-Higgins, M. S. 1960 Mass transport in the boundary-layer at a free oscillating surface. J. Fluid Mech. 8, 293–306.Google Scholar
Longuet-Higgins, M. S. 1969 Action of a variable stress at the surface of water waves. Phys. Fluids 12, 737–740.Google Scholar
Longuet-Higgins, M. S. 1991 Capillary rollers and bores. Proc. IUTAM Symp. on Breaking Waves. Sydney, Australia, 15–19 July 1991.
Ruvinsky, K. D. & Freidman, G. I. 1985a Improvement of the first Stokes method for the investigation of finite-amplitude potential gravity-capillary waves. In 9th All Union Symp. on Diffraction and Propagation Waves, Tbilisi, Theses of Reports vol. 2, pp. 22–25.
Ruvinsky, K. D. & Freidman, G. I. 1985b Ripple generation on capillary-gravity wave crests and its influence on wave propagation. Inst. Appl. Phys. Acad. Sci. USSR Gorky, Preprint N132, 46 pp.Google Scholar
Ruvinsky, K. D. & Freidman, G. I. 1987 The fine structure of strong gravity-capillary waves. In Nonlinear Waves: Structures and Bifurcations (ed. A. V. Gaponov-Grekhov, M. I. Rabinovich pp. 304–326. Moscow: Nauka.
Ruvinsky, K. D., Feldstein, F. I. & Freidman, G. I. 1991 Numerical simulations of the quasi-stationary stage of ripple excitation by steep gravity-capillary waves. J. Fluid Mech. 230, 339–353.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 8–441; reprinted in Mathematica and Physical Papers, Vol. 1, pp. 314–326, Cambridge University Press.Google Scholar