
Journal of the Australian Mathematical Society  Series B
Vol. 40 Part 2 (1998)
On the scattering of water waves by a submerged
slender barrier
P. K. Kundu
Department of Applied Mathematics, Vidyasagar University
Midnapore721102, INDIA
and
N. K. Saha
Department of Mathematics, Bhatter College, P.O.: Dantan, Distt.
Midnapore (W.B.), INDIA
Abstract:
An approximate analysis, based on the standard perturbation
technique, is described in this paper to find the corrections, up to
first order to the reflection and transmission coefficients for the
scattering of water waves by a submerged slender barrier, of finite
length, in deep water. Analytical expressions for these corrections
for a submerged nearly vertical plate as well as for a submerged
vertically symmetric slender barrier of finite length are also
deduced, as special cases, and identified with the known results. It
is verified, analytically, that there is no first order correction
to the transmitted wave at any frequency for a submerged nearly
vertical plate. Computations for the reflection and transmission
coefficients up to O
,
where
is a small dimensionless
quantity, are also performed and presented in the form of both
graphs and tables.
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© Copyright 1998, Australian Mathematical Society
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