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1 International Journal of Applied Mechanics and Engineering

1 2010

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Interface wave diffraction by bottom undulations in the presence of a thin plate submerged in lower fluid

Dolai D. P., Dolai P.

International Journal of Applied Mechanics and Engineering

2010

Vol. 15, no 4

1017-1036

The problem of interface wave diffraction by bottom undulations in the presence of a thin vertical plate is investigated in this paper. The plate is submerged in the lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green's integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical plate present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and suitable application of multi-term Galerkin approximations. The numerical results of zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature of first-order reflection coefficient due to multiple interaction of the incident wave with bottom undulations is observed. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.