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Water wave diffraction by a surface strip

Published online by Cambridge University Press:  04 January 2007

RUPANWITA GAYEN ,
B. N. MANDAL  and
A. CHAKRABARTI
RUPANWITA GAYEN
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108, India
B. N. MANDAL*
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108, India
A. CHAKRABARTI
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
*
†Author to whom correspondence should be addressed: biren@isical.ac.in
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Abstract

The two-dimensional problem of wave diffraction by a strip of arbitrary width is investigated here in the context of linearized theory of water waves by reducing it to a pair of Carleman-type singular integral equations. These integral equations have been solved earlier by an iterative process which is valid only for a sufficiently wide strip. A new method is described here by which solutions of these integral equations are determined by solving a set of four Fredholm integral equations of the second kind, and the process is valid for a strip of arbitrary width. Numerical solutions of these Fredholm integral equations are utilized to obtain fairly accurate numerical estimates for the reflection and transmission coefficients. Previous numerical results for a wide strip are recovered from the present analysis. Additional results for the reflection coefficient are presented graphically for moderate values of the strip width which exhibit a less oscillatory nature of the curve than the case of a wide strip.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 419 - 438
Copyright
Copyright © Cambridge University Press 2007

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References

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