大范围波浪传播数学模型

南黄海辐射沙脊群海域范围广阔、海底地形变化剧烈。在传统缓坡方程基础上建立的波浪传播数学模型难以计算该海域的波浪场。为了解决此问题,文章在洪广文推导的缓坡方程推广形式的基础上,改进了数值计算方法,建立了大范围波浪传播数学模型。运用波数矢无旋性方程,将缓坡方程转化为波作用守恒方程和光程函数方程,从而消除了波长对计算步长的限制。运用硬盘同步记录法,把求解时所需要的内存用量转化为硬盘用量,从而可以运用高分辨率网格计算大范围海域。在南黄海辐射沙脊群的应用表明,该模型适用于大范围、复杂水下地形的波浪场计算。

Mathematical model of wave transformation for large calculation domain

Radial sand ridge field locates on the continental shelf of South Yellow Sea, which covers large areas and the topography varies greatly from place to place.The wave transformation models,established on the traditional mild slope equation,have difficulty to calculate this wave field.In order to solve this problem,an enhanced numerical method was introduced in this paper.According to the methods used before, a.wave refraction diffraction model was set up.Firstly,mild slope equation should be transformed into the wave action conservation equation and wave eikonal equation by introducing the irrotationality equation,so that the restriction of wave length to calculation step can be eliminated.Secondly ,fine mesh should be used,which can accurately reflect the relationship between topography and wave transformation.Besides,PC requires huge memory space to calculate large water area with fine mesh.But now a newly developed bookkeeping procedure can solve this problem.It changes the requirement of computer memory space into the need of hard-disk-size.As a result,the size of calculation domain is enlarged and the resolution of mesh isalso enhanced at the same time.The application of this model in the region of the radial sand ridge field suggests that it is available in the analysis of wave refraction-diffraction effects under natural sea conditions.