波浪在局部可渗透水平海床上传播的解析解

本文建立了波浪在局部可渗透水平海床上传播的解析解，并研究了波浪在局部可渗透海床上的透射、反射问题。研究中将计算域划分为4个区域，中间区域为流域，海底可渗透，其下区域为多孔介质海床，左右两个区域也为流域，但海底不可渗透。应用线性波浪理论，建立了各流域包含非传播模态的速度势表达式，给出了海床内部的压强表达式，并利用交界面上匹配条件，求解了表达式中的待定系数。基于该解析模型，探讨了海床渗透系数、相对水深、渗透海床长度对波浪传播变形的影响。结果表明，波高沿程衰减，强度随渗透系数、渗透海床长度的增加以及相对水深的减小而变大；局部可渗透海床会引起波浪的反射和透射，随着海床长度的增加，反射系数振荡变化，并最终趋于常数，透射系数指数衰减，并最终趋于0。

Analytical solution for waves propagating over a local permeable seabed

The present study is concerned with the analytical solution for waves propagating over a local permeable seabed and wave reflection and transmission by the local permeable seabed. The computational domain is decomposed into four subdomains of which the middle subdomain is permeable, with the porous seabed beneath it, and the left and right subdomains are impermeable. Applying the linear wave theory, the velocity potential of each fluid subdomain is set up, including the effect of evanescent mode, and the pressure inside the porous seabed is given. The unknowns are solved by the continuous conditions at the interfaces between the neighboring subdomains. The effect of permeability coefficient, water depth and length of permeable seabed on wave transformation is discussed. The results indicate the wave height attenuates increasingly with the increase of permeability coefficient, the length of permeable seabed, and decrease of water depth. Wave reflection and transmission will occur due to the local permeable seabed. The reflection coefficient oscillates, and tends to be constant eventually, while the transmission coefficient reduces exponentially, and tends to be zero with the increase in the length of permeable seabed.