Stability properties of steady water waves with vorticity

We present two stability analyses for exact periodic traveling water waves with vorticity. The first approach leads in particular to linear stability properties of water waves for which the vorticity decreases with depth. The second approach leads to a formal stability property for long water waves...

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Veröffentlicht in:	Communications on pure and applied mathematics 2007-06, Vol.60 (6), p.911-950
Hauptverfasser:	Constantin, Adrian, Strauss, Walter A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Computational methods in fluid dynamics Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Mathematics Partial differential equations Physics Sciences and techniques of general use
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Zusammenfassung:	We present two stability analyses for exact periodic traveling water waves with vorticity. The first approach leads in particular to linear stability properties of water waves for which the vorticity decreases with depth. The second approach leads to a formal stability property for long water waves that have small vorticity and amplitude although we do not use a small‐amplitude or long‐wave approximation. © 2006 Wiley Periodicals, Inc.
ISSN:	0010-3640 1097-0312
DOI:	10.1002/cpa.20165