Author:
Longuet-Higgins Michael S.
Abstract
The existence of steady solitary waves on deep water was suggested on physical grounds by Longuet-Higgins (1988) and later confirmed by numerical computation (Longuet-Higgins 1989; Vanden-Broeck & Dias 1992). Their numerical methods are accurate only for waves of finite amplitude. In this paper we show that solitary capillary-gravity waves of small amplitude are in fact a special case of envelope solitons, namely those having a carrier wave of length 2π(T/ρg)1½2 (g = gravity, T = surface tension, ρ = density). The dispersion relation $c^2 = 2(1-\frac{11}{32}\alpha^2_{\max)$ between the speed c and the maximum surface slope αmax is derived from the nonlinear Schrödinger equation for deep-water solitons (Djordjevik & Redekopp 1977) and is found to provide a good asymptote for the numerical calculations.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference11 articles.
1. Djordjevik, V. D. & Redekopp, L. G. 1977 On two-dimensional packets of capillary—gravity waves.J. Fluid Mech. 79,703–714.
2. Longuet-Higgins, M. S. 1989 Capillary—gravity waves of solitary type on deep water.J. Fluid Mech. 200 451–470 (referred to herein as LH21.
3. Vanden-Broeck, J.-M. & Dias, F. 1992 Gravity—capillary solitary waves in water of infinite depth and related free surface flows.J. Fluid Mech. 240 549–557 (referred to herein as VBD1.
4. Longuet-Higgins, M. S. 1988 Limiting forms for capillary—gravity waves.J. Fluid Mech. 194,351–375.
5. Ablowitz, M. J. & Segur, H. 1979 On the evolution of packets of water waves.J. Fluid Mech. 92,691–715.
Cited by
57 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献