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Stability properties of steady water waves with vorticity
Author(s) -
Constantin Adrian,
Strauss Walter A.
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20165
Subject(s) - vorticity , amplitude , stability (learning theory) , mathematics , potential vorticity , mathematical analysis , positive vorticity advection , vorticity equation , mechanics , physics , vortex , optics , machine learning , computer science
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.