Author:
Marchant T. R.,Smyth N. F.
Abstract
The extended Korteweg-de Vries equation which includes nonlinear and dispersive terms cubic in the wave amplitude is derived from the water-wave equations and the Lagrangian for the water-wave equations. For the special case in which only the higher-order nonlinear term is retained, the extended Korteweg-de Vries equation is transformed into the Korteweg-de Vries equation. Modulation equations for this equation are then derived from the modulation equations for the Korteweg-de Vries equation and the undular bore solution of the extended Korteweg-de Vries equation is found as a simple wave solution of these modulation equations. The modulation equations are also used to extend the solution for the resonant flow of a fluid over topography. This resonant flow occurs when, in the weakly nonlinear, long-wave limit, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. In addition to the effect of higher-order terms, the effect of boundary-layer viscosity is also considered. These solutions (with and without viscosity) are compared with recent experimental and numerical results.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference31 articles.
1. Laitone, E. V. :1960 The second approximation to cnoidal and solitary waves.J. Fluid Mech. 9,430–444.
2. Whitham, G. B. :1965b Non-linear dispersive waves.Proc. R. Soc. Lond. A283,238–261.
3. Akylas, T. R. :1984 On the excitation of long nonlinear water waves by a moving pressure distribution.J. Fluid Mech. 141,455–466.
4. Grimshaw, R. H. J. & Smyth, N. F. 1986 Resonant flow of a stratified fluid over topography.J. Fluid Mech. 169,429–464.
5. Miles, J. W. :1979 On internal solitary waves.Tellus 31,456–462.
Cited by
102 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