A non-local formulation of rotational water waves
A non-local formulation of rotational water waves
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DOI：
10.1017/jfm.2011.404
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发表时间：
2011-12-01
影响因子：
3.7
通讯作者：
Fokas, A. S.
中科院分区：
文献类型：
--
作者：
Ashton, A. C. L.;Fokas, A. S.
无旋水波的经典方程最近被重新表述为两个方程的系统，其中之一是一个显式的非局部方程的波高和速度势上的自由表面上评估。本文在二维情况下：（a）将有关公式推广到常涡量的情况，以及自由面由多值函数描述的情况;（B）在行波情况下，我们导出自由面的上界;（c）第（1）款在常涡的情况下，我们构造了一系列近似哈密顿系统，它们提供了某些物理量的渐近极限的近似。小参数。特别是，明确的涡度的Korteweg-de弗里斯方程的系数的依赖关系被澄清。
The 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.