浅水孤立波在三维浮体上的绕射

浅水域中非线性水波运动的控制方程通常是经过深度平均的Boussinesq方程。然而,这一方程在浮体近旁或水下障碍物附近不再适用,在这些区域,流动在水深方向的变化不容忽略,本文应用匹配渐近展开法和边缘层(edge layer)思想,建立了浅水弱非线性波与三维浮体相互作用的数学模型,作为算例,求解了浅水孤立波在垂直圆柱形浮体上的绕射.本方法可以推广到波在一般浮体上绕射的情况。

THE DIFFRACTION OF SOLITARY WATER WAVE ON THREE-DIMENSIONAL FLOATING BO DIES

Depth averaged Boussinesj equations are usually used as governning equations for the nonlinear water wave motions in shallow water. These equations, however, are not applied in the vicinity of floating bodies or underwater" obstacles, in which the variation of the fluid flow in depth cannot be ignored.By using the method of matched asymptotic expansions and the idea of edge layer, a mathematical model for describing the interaction between weakly nonlinear shallow water waves and three-dimensional floating bodies is formed in the paper. ,As a numerical example, the dif-. fraction of a solitary wave on a floating circular Cylinder has been investigated and the results are presented. The present method may be further extended to suit for the diffraction of waves on floating bodies with general shapes.