A new type of three-dimensional deep-water wave of permanent form-Reference-Cited by-同舟云学术

A new type of three-dimensional deep-water wave of permanent form

Published:1980-12-29 Issue:4 Volume:101 Page:797-808
ISSN:0022-1120
Container-title:Journal of Fluid Mechanics
language:en
Short-container-title:J. Fluid Mech.

Author:

Saffman Philip G.,Yuen Henry C.

Abstract

A new class of three-dimensional, deep-water gravity waves of permanent form has been found using an equation valid for weakly nonlinear waves due to Zakharov (1968). These solutions appear as bifurcations from the uniform two-dimensional wave train. The critical wave heights are given as functions of the modulation wave vector. The three-dimensional patterns may be skewed or symmetrical. An example of the skewed wave pattern is given and shown to be stable. The results become exact in the limit of very oblique modulations.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference8 articles.

1. Schwartz, L. W. 1974 Computer extension and analytic continuation of Stokes expansion for gravity waves.J. Fluid Mech. 62,553–478.

2. Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid.J. Appl. Mech. Tech. Phys. 2,190–194.

3. Peregrine, D. H. & Thomas, G. P. 1979 Finite amplitude deep water waves on currents.Phil. Trans. Roy. Soc. A 292,371–390.

4. Crawford, D. R. , Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves.Wave Motion 2,1–16.

5. Chen, B. & Saffman, P. G. 1980 Numerical evidence for the existence of new types of gravity waves of permanent form on deep water.Stud. Appl. Math. 62,1–21.

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