Generation of surface waves by shear-flow instability

TitleGeneration of surface waves by shear-flow instability
Publication TypeJournal Article
Year of Publication2014
AuthorsYoung W.R, Wolfe CL
JournalJournal of Fluid Mechanics
Volume739
Pagination276-307
Date Published2014/01
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000331624200013
Keywordscapillary waves; critical layers; evolution; gravity-capillary waves; growth; layer; profile; stability; water; waves/free-surface flows; wind
Abstract

We consider the linear stability of an inviscid parallel shear flow of air over water with gravity and capillarity. The velocity profile in the air is monotonically increasing upwards from the sea surface and is convex, while the velocity in the water is monotonically decreasing from the surface and is concave. An archetypical example, the 'double-exponential' profile, is solved analytically and studied in detail. We show that there are two types of unstable mode which can, in some cases, co-exist. The first type is the 'Miles mode' resulting from a resonant interaction between a surface gravity wave and a critical level in the air. The second unstable mode is an interaction between surface gravity waves and a critical level in the water, resulting in the growth of ripples. The gravity capillary waves participating in this second resonance have negative intrinsic phase speed, but are Doppler shifted so that their actual phase speed is positive, and matches the speed of the base-state current at the critical level. In both cases, the Reynolds stresses of an exponentially growing wave transfer momentum from the vicinity of the critical level to the zone between the crests and troughs of a surface wave.

DOI10.1017/jfm.2013.617
Short TitleJ. Fluid Mech.
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Student Publication: 
No