坡度、水深和波高对孤立波分裂影响作用的数值研究

A numerical study of influences of slope, water depth and wave height on the solitary wave fission

基于有限差分法建立高阶Boussinesq方程的一维数值模型,时间步进上采用三阶预报、四阶校正格式。在验证数值模型适用性的基础上研究了坡度、水深和波高对孤立波分裂位置、主峰和次峰波高大小的影响,证明了孤立波的分裂与非线性特征有关。坡度缓,非线性演化的时间长,孤立波更易分裂,但坡度变缓不会明显增强波浪非线性特征,从而对主、次峰波高影响不大;入射波高大、水深浅(深水水深或浅水水深)的孤立波非线性特征更强,波形更尖锐,孤立波更易发生分裂,且主、次峰波高也越大。

Based on Boussinesq equation, a one-dimensional numerical model is established by using finite difference method and the governing equation is solved with third-order predictor and fourth-order corrector method in the time marching. The model is validated to study the influences of slope, water depth and wave height on locations of wave fission and magnitude of wave height. The results show that fission process is related to non-linear character. The fission process happens more easily at the milder slope, on which the wave non-linear character is slightly enhanced. The solitary wave with larger incoming wave height or smaller water depthwhich includes deep and shallow water depths, has stronger non-linear character and more easily splits into several waves which have larger wave height.