Oblique water wave diffraction by thin vertical barriers in water of uniform finite depth

A train of small-amplitude surface waves is obliquely incident on a fixed, thin, vertical plate submerged in deep water. The plate is infinitely long in the horizontal direction. An appropriate one-term Galerkin approximation is employed to calculate very accurate upper and lower bounds for the reflection and transmission coefficients for any angle of incidence and any wave number thereby producing very accurate numerical results.

Oblique diffraction of surface waves by a submerged vertical plate

Velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodal(y along its length. The technique of deriving the potentials here is an extension of the technique used for the case of only time harmonic vertical line source. The present case is concerned with the two-dimensional modified Helmholtz's equation while the previous is concerned with the two-dimenslonal Laplace's equation.

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Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz's equation

The problem of oblique scattering by fixed thin vertical plate submerged in deep water is studied here, assuming linear theory, by employing single-term Galerkin approximation involving constant as basis multiplied by appropriate weight function after reducing it to solving a pair of first kind integral equations. Upper and lower bounds of reflection and transmission coefficients when evaluated numerically are seen to be very close so that their averages produce fairly accurate numerical estimates for these coefficients. Numerical estimates for the reflection coefficient are depicted graphically against the wave number for different values of various parameters. The numerical results obtained by the present method are found to be in an excellent agreement with the known results.

B. N. Mandal

Papers

A Note on the Scattering of Surface Wave Obliquely Incident on a Submerged Fixed Vertical Barrier