高阶孤立波的速度场特征

Velocity Field of High Order Solitary Wave

采用完全非线性高度色散水波理论,运用约化摄动展开法并运用符号运算工具,得到孤立波十七阶渐近解。基于高阶孤立波解,分析比较了孤立波自由表面水平流速、水深平均水平流速、底部水平流速之间的差异,并且与现有的完全非线性数值解进行了比较。当波幅较大时,孤立波的三阶孤立波解与本文的高阶解比较接近。在波峰附近,自由液面的水平流速大于水深平均流速,而在离波峰较远处自由液面的水平流速小于水深平均流速。

An exact fully nonlinear and fully dispersive （FNFD） model was used to study high order solita-ry wave. Using the reductive perturbation method, the leading 17th-order solitary wave solutions were obtained. Using these solutions, the difference among the horizontal velocity on the free surface, the depth-averaged velocity and the velocity on the bottom were discussed and compared with the numerical results. It turns out that the horizontal velocities, evaluated at the free surface and the, bottom, are of sig-nificant difference with the depth-averaged value.