A note on the growth of small-scale Langmuir circulations

Abstract

The processes responsible for the generation of the vorticity in Langmuir circulations are unknown. Perhaps the most elementary and attractive proposition suggests that longitudinal vorticity is produced by the distortion of the cross-wind vorticity of the mean wind-driven surface currents by Reynold's stresses due to short-crested gravity waves. This suggestion, made by Ichiye (1967), and by Kraus (1967) in a somewhat different proposal, is the heart of a recent theory proposed by Craik (1970). In this paper, Craik's assumptions concerning the relative magnitudes of the waves and current are criticized, and it is shown that for Langmuir circulations the interaction between the two should occur at a higher order. By concentrating on vortex line deformations the necessary modifications are calculated. Viewed in this way, the proposed mechanism is so simple that its consequences can be easily explored. The principal consequence is that no inviscid mechanism by which the cross-stream vorticity is distorted (by waves or any other means) to produce longitudinal vorticity appears to be consistent with the observed facts. Langmuir circulations are therefore likely to be more intricate than Craik supposed.