渗透海床上波浪传播特性的研究

Research of the characteristics of wave propagation over porous bottom

波浪在渗透海床上传播时会发生波高的衰减。基于Dean和Dalrymple(1984年)提出的渗透海床上波浪传播的理论模型,推导了波浪运动的速度势表达式和色散关系,并采用迭代方法,提出了一种求解色散方程的简单高效的数值算法,从而求得波浪的空间衰减系数(即复波数虚部)。在此基础之上,研究了不同渗透系数和不同水深条件下波高的衰减规律,结果表明,波浪在传播过程中波高按指数衰减,衰减速率随渗透系数的增大和相对水深的减小而增大,但由于波浪的空间衰减系数较小,波浪的衰减也较为缓慢,通常情况下,只有当波浪长距离传播时,海床渗透导致的波高衰减才较为显著。

Wave damping is a common phenomenon as wave propagation over porous medium. Base on Dean and Dalrymple＇s theoretical results of wave propagation over rigid, porous bottom, the velocity potential and the dispersion relationship are derived. With iterative approach, a simple and efficient numerical algorithm is proposed to solve the dispersion relationship, getting the space damping coefficient, namely the image part of complex wave number. Then, the rules of wave damping under the conditions of different permeability coefficients and water depth are studied. The results indicate that wave height attenuates exponentially in the propagation over porous bottom, and the damping rate increases with an increase in permeability coefficient and a decrease in water depth. However, the space damping coefficient is small, leading to a slow attenuation of wave height. In general, only when the wave propagates over long distances in a permeable bottom will the wave damping be obvious.