Abstract
The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.
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Sandip Paul was born in 1983. He is a assistant professor at Department Mathematics, Adamas Institute Technology, Kolkata, India. His current research interests include water wave problems.
Soumen De was born in 1981. He is a assistant professor at the Department Applied Mathematics, University of Calcutta, India. His current research interests include water wave problems, integral equations, etc.
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Paul, S., De, S. Wave scattering by porous bottom undulation in a two layered channel. J. Marine. Sci. Appl. 13, 355–361 (2014). https://doi.org/10.1007/s11804-014-1276-4
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DOI: https://doi.org/10.1007/s11804-014-1276-4