International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 113-125
doi:10.1155/S0161171285000102
scattering of surface waves by a half immersed circular cylinder in fluid of finite depth
1Department of Applied Mathematics, University College of Science, 92 A.P.C. Road, Calcutta 700 009, India
2Department of Mathematics, Presidency College, Calcutta 700 073, India
Received 19 November 1982
Copyright © 1985 Birendranath Mandel and Sudip Kumar Goswami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A train of surface waves is normally incident on a half immersed circular cylinder in a fluid of finite depth. Assuming the linearized theory of fluid under gravity an integral equation for the scattered velocity potential on the half immersed surface of the cylinder is obtained. It has not been found possible to solve this in closed form even for infinite depth of fluid. Our purpose is to obtain the asymptotic effect of finite depth “h” on the transmission and reflection coefficients when the depth is large. It is shown that the corrections to be added to the infinite depth results of these coefficients can be expressed as algebraic series in powers of a/h starting with (a/h)2 where “a” is the radius of the circular cylinder. It is also shown that the coefficients of (a/h)2 in these corrections do not vanish identically.