On Wilton's ripples: a special case of resonant interactions

Author:

McGoldrick L. F.

Abstract

The phenomenon of second harmonic resonance for capillary-gravity waves is reconsidered here by the asymptotic method of multiple time and space scales. The periodic finite amplitude waves of permanent form found by Wilton in 1915 which correspond to this configuration are shown to be no more than a special case of the more general resonant interaction theory, and owe their existence to a critical choice of initial conditions. It is further suggested that the influence of viscous dissipation will render this solution virtually undetectable in a real liquid.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference6 articles.

1. Pierson, W. J. & Fife, P. 1961 Some non-linear properties of long-crested periodic waves with lengths near 244 centimetres.J. Geophys. Res. 66,163–179.

2. Wilton, J. R. 1915 On ripples.Phil. Mag. (6)29,688–700.

3. Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Waltham, Mass.:Blaisdell-Ginn.

4. Mcgoldrick, L. F. 1970 An experiment on capillary-gravity resonant wave interactions.J. Fluid Mech. 40,251–271.

5. Mcgoldrick, L. F. 1965 Resonant interactions among capillary-gravity waves.J. Fluid Mech. 21,305–331.

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