变深度非均匀流中非线性重力波调制理论

THE MODULATIONAL THEORY OF NONLINEAR GRAVITY-WAVE IN FLUID WITH VARYING DEPTH AND NONUNIFORM CURRENT

摘要

摘要:本文考虑了缓变水深和缓变流对Stokes波包的影响,用WKB展开式推导出一个新的任意水深的四阶波包演化方程,推广了Turpin等人的有限水深三阶Schrdinger方程,在常深度无流条件下,新方程同U Brinch—Nielsen等人的无流任意常水深四阶方程的二维形式完全一致;此外,我们用差分法研究了变地形和流对孤立波包演化的影响。

Abstract:Using the method of multiple scales and WKB expansion a new fourth order evolution equation of amplitude of Stokes wave train in two-dimensional fluid with slowly varying depth and current has been derived. Effects of varying depth and current OB the-evolution of a single envelope have been calculated by the finite-difference method.