Journal of Applied Mathematics
Volume 2006 (2006), Article ID 53723, 24 pages
A study of the waves and boundary layers due to a surface pressure on a uniform stream of a slightly viscous liquid of finite depth
Department of Mathematics, Khalisani College, Hooghly 712 138, India
Received 31 May 2006; Revised 25 October 2006; Accepted 22 November 2006
Copyright © 2006 Arghya Bandyopadhyay. 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.
The 2D problem of linear waves generated by an arbitrary pressure distribution on a uniform viscous stream of finite depth is
examined. The surface displacement is expressed correct to terms, for small viscosity
, with a restriction on . For , exact forms of the steady-state propagating waves are next obtained for all
and not merely for which form a wave-quartet or a wave-duo amid local disturbances. The long-distance asymptotic forms are then shown to be uniformly valid for large . For numerical and other purposes, a result essentially due to Cayley is used successfully to express these asymptotic forms in a series of powers of powers of or with coefficients expressed directly in terms of nonviscous wave frequencies and amplitudes. An approximate thickness of surface boundary layer is obtained and a numerical study is undertaken to bring out the salient features of the exact and asymptotic wave motion in question.