Approximate analytical solutions for a solitary wave interacting with a partially submerged porous wall

This study presents the development of an approximate analytical model for the investigation of the hydrodynamic interactions between a solitary wave and a partially submerged thin porous wall. Analytical solutions of the velocity potentials are derived according to the Fourier integral and solution superposition procedure along with satisfying the formed boundary and matching conditions. The free-surface elevations are also formulated. The hydrodynamic forces are computed by integrating the pressure distributions along the structural surfaces. Laboratory experiments were carried out to measure the free-surface elevations at locations upstream and downstream of the porous walls tested for the verification of the derived analytical solutions. It is demonstrated through result comparisons that the present analytical model can provide nicely matched predictions on the time varying transmitted waves including wave peak but slightly overestimated reflected wave heights. The horizontal hydrodynamic forces from the present analytical solutions are also in good agreement with other published experimental data when a special case of non-porous wall is considered. The variations of wave run-up, overall transmission coefficient, and maximum horizontal force under different conditions are presented and discussed to evaluate the performance of a partially submerged thin porous wall subject to an encountering solitary wave.