Water wave interaction with two symmetric inclined permeable plates

• Wave interaction with two symmetric inclined porous plates is investigated.
• The physical quantities are computed using the solutions of two second kind hypersingular integral equations.
• Adjusting the distance between the plates and their angle of inclination, results for a single horizontal plate are recovered.
• That the present approach can be employed to a moored flexible porous plate, is outlined briefly.
• Numerical results for R, J, F and M are discussed through graphical presentations.

We consider the reflection and the transmission of the surface water waves by two inclined identical permeable plates that are symmetric with respect to a line which is perpendicular to the horizontal line connecting the middle points of the plates. The problem is reduced to finding the solutions of two hypersingular integral equations of the second kind for the discontinuity in the velocity potential across one of the plates. The unknowns of the integral equations are expanded in terms of a finite series of Chebyshev polynomials multiplied by an appropriate weight function and then solved by collocating at suitable discrete points. Using these solutions, the numerical estimates for the reflection and the transmission coefficients, amplitudes of the hydrodynamic forces and moments and the wave dissipation coefficient are computed. Numerical results for these quantities are presented graphically in a number of figures. These results are compared with the published results for a single vertical as well as horizontal permeable plates and a submerged horizontal impermeable plate.