Ni, Y.-L.; Xie, T., and Gong, M., 2020. Analytical solution for waves propagating over local permeable seabed of constant water depth. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 294-298. Coconut Creek (Florida), ISSN 0749-0208.
The present study is concerned with the analytical solution for waves propagating over a local permeable seabed of constant water depth and wave reflection and transmission by the local permeable seabed. The fluid domain is decomposed in three subdomains of which the middle subdomain is permeable and the left and right subdomains are impermeable. Applying the linear wave theory and Darcy's law, the velocity potential of each subdomain is set up, including the effect of evanescent mode. Then, the perturbation method proposed by Mendez is used to obtain the complex wave number and the roots of evanescent mode, and the unknowns in the velocity potential are solved by the continuous conditions at the interfaces between the neighboring subdomains. Based on this analytical model, the effect of permeability coefficient, water depth and length of permeable seabed on wave propagation and 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. And the wave height curve oscillates around the exponential decay curve for the entire permeable seabed proposed by Dean and Dalrymple. This is the result of wave reflection and transmission induced by the local permeable seabed. The reflection coefficient is close to zero when the length of the permeable seabed is an integer multiply of a half wavelength, and it reaches the maximum value when the length of the permeable seabed is odd times of one quarter of the wavelength. The transmission coefficient reduces exponentially with the length increasing in permeable seabed.