高阶涌潮方程的一种数值方法

涌潮潮头处,水位骤涨,相应地,流速的铅垂分量必有一定大小.考虑这个分量以后,压力不再符合静水压力分布律,据此可以得到高阶浅水流动方程.采用龙格库塔法求该方程的数值解.结果表明,强度较小时,涌潮是表面光滑,波幅渐次减小的波列,强度大到一定程度,表面破碎,进而发展成为溯源推进的水滚.

A numerical method of high-order bore equation

At the bore, water level rises rapidly, accordingly, vertical component of velocity must be considered.In this case, the flow should be described by high-order sallow water flow equation. In this paper, the equation is solved by Runge-Kutta method. The result reveals that if the bore is weak, it becomes a wave train whose surface is smooth, and amplitude is decreased gradually.If the bore is strengthened to the degree of breaking, it is evolved into a roll bore.