The Scattering of Water Waves by <i>M</i>-Floating Porous Plates Over (<i>M</i> − 1) Trenches

Abstract This article investigates the interaction of water waves with multiple thin horizontal floating porous plates over multiple trenches at the bottom. Here, the horizontal floating porous plates are placed at a finite distance from each other, and the trenches are in between the plates. Using the linearized theory of water waves, the boundary value problem is solved for velocity potential using Havelock’s expansion and algebraic least-square method. To understand the advantage of multiple porous plates and trenches, the numerical results are plotted for the scattering and dissipation coefficients through different graphs to examine the effect of various parameters. In the direction of the use of a minimal number of porous plates in the absence of trenches, it is observed that the curves almost coincide for the three and four-plate cases, implying three plates will be sufficient for maximum wave energy dissipation and minimal wave transmission. But, for the case of two trenches and in the absence of porous plates, the curves show an oscillatory pattern with harmonic and subharmonic peaks. The study also shows that the oscillating pattern in the curves vanishes when there are two trenches and three porous plates with moderate values of the porous-effect parameter. In the latter case, plates with larger lengths will produce almost zero transmission and dissipate or reflect a major part of the incident wave energy. It is concluded that the above-specific combination of barriers and plates dissipates maximum wave energy and transmits a small amount, providing a safer zone in the trench regions. Thus, multiple navigation channels can be created to overcome the issues of dense vessel traffic arising in a single channel.