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Effects of viscosity on linear gravity waves due to surface disturbances in water of finite depth
Author(s) -
Bandyopadhyay A.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310020
Subject(s) - viscosity , laplace transform , mathematical analysis , mathematics , displacement (psychology) , constant (computer programming) , surface (topology) , mechanics , laplace pressure , surface gravity , physics , geometry , thermodynamics , surface tension , computer science , psychology , astronomy , psychotherapist , programming language , spectral line
The three‐dimensional problem of waves due to an arbitrary initial time‐dependent surface pressure together with an elevation of the surface in a viscous fluid of constant finite depth h is examined. It is shown that the multiple‐integral expression for the surface displacement ζ is reducible to one which is correct to terms of order O (ν'), ν' = ν/(4 gh 3 ) 1/2 , for small coefficient of viscosity ν, under certain conditions. When the Laplace inversion is completed in ζ we arrive at new results which differ significantly from those obtained in an earlier analysis of the problem by Nikitin and Potetyunko [1].