A Depth‐Dependent Current and Wave Interaction Model in the Presence of Porous Seabed

Abstract

This study develops a three‐dimensional model to describe wave–current interactions over a seabed featuring a porous layer with spatially varying thickness. A previous approach (Hsu et al., 2018, https://doi.org/10.1016/j.coastaleng.2018.06.003 ) addressed energy dissipation within the porous medium by introducing a complex‐valued group velocity and representing energy transport through its real part; however, this treatment lacked solid physical justification and relied on an empirical damping coefficient within the phase‐averaged wave model. The present work extends Mellor's (2008, https://doi.org/10.1175/2008jpo3971.1 ) depth‐resolved formulation, originally devised for impermeable seabeds, to incorporate the effects of a porous layer. The solution is explicitly decomposed into wave and current components. For the wave part, eigenfunctions based on linear wave theory are used to characterize wave motion in both the fluid and porous regions. By applying a phase‐averaging technique, analytical expressions are derived for essential quantities such as the real‐valued dynamic and kinematic group velocities, radiation stresses, drift velocity, and energy dissipation within the porous medium. This theoretical foundation is suitable for integration into existing numerical models that simulate wave–current interactions over porous seabeds and reef environments. Several numerical results are presented and discussed for the dynamic and kinematic group velocities, as well as for the temporal modification factor of wave energy under various porous parameters. The numerical evidence shows that the proposed theory can contribute up to for shallow water waves propagating over a thick porous layer of high porosity. In addition, the formulations of the energy sinks are implemented to simulate wave damping over porous breakwaters.