Effects of viscosity on linear gravity waves due to surface disturbances in water of finite depth | Zendy

Bandyopadhyay A. | Zendy

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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].

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