Scattering of water waves in the presence of multiple porous structures over trench-type bottom topography

The present study examines the effectiveness of multiple finite-width porous structures in mitigating wave impact on the shorelines featuring trench-type bottom seabed. Wave propagation through thick porous structures is represented using the Sollitt and Cross model, utilizing the principles of small-amplitude water wave theory. The boundary value problem is converted into a system of linear algebraic equations through the eigenfunction expansion method, which is then solved numerically. The findings indicate that increasing the number of porous structures and trenches enhances wave reflection while reducing wave transmission. Analysis of the reflection coefficient's variation with wavenumber for various numbers of trenches and porous structures shows that wave reflection exhibits harmonic peaks followed by subharmonic peaks, with the amplitude of these peaks increasing up to certain wavenumbers before diminishing for higher wavenumbers. The scattering coefficients exhibit oscillatory and periodic patterns in response to changes in the spacing between trenches, porous structures, and the distance from the last trench to the first porous structure. Additionally, oscillatory and periodic patterns are observed in scattering coefficients as a function of trench width. In contrast, as the width of the porous structures increases, the wave reflection exhibits an oscillatory increasing pattern before eventually stabilizing at larger widths. Meanwhile, the transmission coefficient decreases and ultimately becomes zero. Furthermore, higher frictional coefficients result in an increased wave reflection and decreased wave transmission. However, a lower free surface elevation in the lee-side region Rt compared to the region R1 occurs due to multiple porous structures and trenches. With three trenches and four porous structures, the transmission coefficient is reduced to less than 3%, leading to a negligible free surface elevation in Rt. Notably, as the number of porous structures increases, the free surface elevation on the lee-side continues to decrease, even when the quantity of rubble mounds remains constant. This study underscores the potential of multiple porous structures in combination with trench-type bottoms for effective coastal protection.