深水有限振幅重力波的一种解法

A SOLUTION OF THE GRAVITY WAVE OF FINITE AMPLITUDE IN DEEP WATER

采用变量代换的方法,处理水波的自由边界,获得了新的水波控制方程和边界条件。以摄动法解非线性偏微分方程的近似解析解,求得了与三阶斯托克斯波略有差别的非线性波面和包含振幅的非线性水波色散关系,并且得出了二阶以上的波动势函数在深水情况下不为零的结论。

the method of variable substitution in the water-wave equation and boundary conditions, this paper deals with the free-surface of the water-wave. The changed water-wave equation and boundary conditions may be written in the formThe asymptotic method is applicable to the solution of nonliner wave. Third order STOKES wave and nonliner dispersion relation are solved. A new conclusion is derived that the high order solution of the potential function is non-zero in deep water.