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Viscous effects on wave generation by strong winds

Published online by Cambridge University Press:  01 February 2008

A. ZEISEL ,
M. STIASSNIE  and
Y. AGNON
A. ZEISEL
Affiliation:
Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
M. STIASSNIE
Affiliation:
Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Y. AGNON
Affiliation:
Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
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Abstract

This paper deals with the stability of water waves in a shear flow. Both temporal and spatial growth rates are derived. A carefully designed numerical solver enables us to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a friction-velocity of 1 m s−1). The main finding is the appearance of a second unstable mode which often turns out to be the dominant one. A comparison between results from the viscous model (Orr–Sommerfeld equations) and those of the inviscid model (Rayleigh equations), for 18 cm long waves, reveals some similarity in the structure of the eigenfunctions, but a significant difference in the imaginary part of the eigenvalues (i.e. the growth rate). It is found that the growth rate for the viscous model is 10 fold larger than that of the inviscid one.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 343 - 369
Copyright
Copyright © Cambridge University Press 2008

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