EFFECT OF A PERMEABLE OCEAN FLOOR ON WAVE SCATTERING BY A VERTICAL POROUS BARRIER USING THE HYPERSINGULAR INTEGRAL EQUATION METHOD
S. Pal1,2,3, S. Paul1,2, S. De1,3
1Ramakrishna Sarada Mission Vivekananda Vidyabhavan Women’s College, Kolkata, India
2Dr. B. C. Roy Academy of Professional Courses, Durgapur, India
3University of Calcutta, Kolkata, India
Keywords: wave scattering, permeable plate, porous seabed, hypersingular integral equation, reflection coefficient, transmission coefficient, energy identity
Abstract
A two-dimensional problem of water-wave scattering by a completely submerged thin vertical porous barrier in the ocean is considered. The fluid is assumed to be bounded above by a free surface and below by a permeable seabed. Using Green’s integral theorem, the boundary-value problem is reduced to a hypersingular integral equation of the second kind expressed in terms of the potential difference across the plate. The equation is solved numerically using a collocation method with a finite series of Chebyshev polynomials of the second kind. The reflection and transmission coefficients are obtained as integrals involving the potential difference. The energy dissipated by the porous plate is also evaluated. Numerical results for the coefficients are presented, and the corresponding energy identity is verified. A significant effect of dual porosity is observed.
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