Reduction in wave shoaling over a linear transition bottom using a porous medium

• We analyzed the wave shoaling phenomenon for porous structures. • We modified the existence of porous media shallow water equations. • We used the separation variable method to obtain the wave transmission coefficient. • We also apply a staggered finite volume method to solve the model numerically. • Mangroves substantially reduced wave shoaling amplitudes. • Therefore, mangroves act as an emerging porous breakwater. Wave shoaling, which involves an increase in wave amplitude due to changes in water depth, can damage shorelines. To mitigate this damage, we propose using porous structures such as mangrove forests. In this study, we use a mathematical model to examine how mangroves, acting as a porous breakwater, can reduce wave shoaling amplitude. Shallow water equations are used as the governing equations and are modified to account for the presence of porous media. To measure the wave reduction generated by the porous media, the wave transmission coefficient is estimated using analytical and numerical approaches. The separation of variables method and the staggered finite volume method are utilized for each approach, respectively. The numerical results are then validated against the previously obtained analytical solutions. We then vary the friction and porosity parameters, influenced by the presence and extent of porous media, to evaluate their effectiveness in reducing wave shoaling.