On the disappearance of the lowest-order instability for steep gravity waves in finite depth

This paper extends to very large steepness the results of the linear stability analysis of two-dimensional periodic gravity waves over a bottom of uniform depth. Both subharmonic and superharmonic instabilities are investigated. For the case considered herein, it is shown how the lowest-order instab...

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Bibliographic Details
Published in:Physics of fluids (1994) 2003-08, Vol.15 (8), p.2445-2448
Main Authors: Francius, Marc, Kharif, Christian
Format: Article
Language:English
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Summary:This paper extends to very large steepness the results of the linear stability analysis of two-dimensional periodic gravity waves over a bottom of uniform depth. Both subharmonic and superharmonic instabilities are investigated. For the case considered herein, it is shown how the lowest-order instability (class I) completely disappears at a critical wave steepness. These results also confirm numerically a theorem connected with the appearance of superharmonic instabilities in finite depth.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.1589012