Author:
Ashton A. C. L.,Fokas A. S.
Abstract
AbstractThe classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free surface. Here, in the two-dimensional case: (a) we generalize the relevant formulation to the case of constant vorticity, as well as to the case where the free surface is described by a multivalued function; (b) in the case of travelling waves we derive an upper bound for the free surface; (c) in the case of constant vorticity we construct a sequence of nearly Hamiltonian systems which provide an approximation in the asymptotic limit of certain physical small parameters. In particular, the explicit dependence of the vorticity on the coefficients of the Korteweg–de Vries equation is clarified.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
28 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