Effect of bottom undulation on the waves generated due to rolling of a plate
 Puspendu Rakshit,
 Sudeshna Banerjea
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In the present paper, the effect of a small bottom undulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of non uniform finite depth is investigated. A simplified perturbation technique involving a non dimensional parameter characterizing the smallness of the bottom deformation is applied to reduce the given boundary value problem to two independent boundary value problems upto first order. The first boundary value problem corresponds to the problem of water wave generation due to rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of uniform finite depth. This is a well known problem whose solution is available in the literature. From the second boundary value problem, the first order correction to the wave amplitude at infinity is evaluated in terms of the shape function characterizing the bottom undulation, by employing Greenâ€™s integral theorem. For a patch of sinusoidal ripples at the sea bottom, the first order correction to the wave amplitude at infinity for both the configuration of the barrier is then evaluated numerically and illustrated graphically for various values of the wave number. It is observed that resonant interaction of the wave generated, with the sinusoidal bottom undulation occurs when the ratio of twice the wavelength of the sinusoidal ripple to the wave length of waves generated, approaches unity. Also it is found that the resonance increases as the length of the barrier increases.
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 Title
 Effect of bottom undulation on the waves generated due to rolling of a plate
 Journal

Journal of Marine Science and Application
Volume 10, Issue 1 , pp 716
 Cover Date
 20110301
 DOI
 10.1007/s1180401110358
 Print ISSN
 16719433
 Online ISSN
 19935048
 Publisher
 Harbin Engineering University
 Additional Links
 Topics
 Keywords

 bottom undulation
 rolling oscillation
 partially immersed barrier
 submerged plate
 Industry Sectors
 Authors

 Puspendu Rakshit ^{(1)}
 Sudeshna Banerjea ^{(2)}
 Author Affiliations

 1. Deshapran Birendranath Institution for Boys, 198B, S. P. Mukherjee Road, Kolkata, 700026, India
 2. Department of Mathematics, Jadavpur University, Kolkata, 700032, India