Effect of sloping bottom on wave interaction with multiple flexible moored breakwaters

Abstract

Abstract An analytical framework is developed to analyze the interaction of oblique waves with multiple flexible porous breakwaters under the consideration of bottom undulation. The mathematical problem is tackled using the small amplitude water-wave theory, with Darcy's law being applied to account for wave interaction with porous media. The bottom topography is considered to have a finite length, flanked by two semi-infinite sections of uniform bottom. The solution to the boundary value problem is approached by employing the eigenfunction expansion method within the uniform bottom regions. For the varying bottom topography, a modified mild-slope equation (MMSE) is utilized. To address the solution at the slope discontinuity at the bottom, a mass-conserving jump condition is applied. By matching solutions at the interfaces, a set of equations is derived. This system of equations encapsulates the behavior of reflection and transmission coefficients, as well as the force exerted on the breakwaters. These parameters are then investigated across various factors, such as the length of the varying bottom, depth ratio, angle of the mooring line, angle of incidence, and flexural rigidity. Graphical representations of the reflection and transmission coefficients, along with the breakwater force, provide insights into the system's behavior under different conditions. The water wave energy can be dissipated for the the optimum values of flexural rigidity. The transmission coefficient is observed to be least for higher mooring angle.