The Breakup of Langmuir Circulation and the Instability of an Array of Vortices

Abstract

The presence and pattern of Langmuir circulation can be detected using side-scan sonar. The circulation creates bands of subsurface bubbles, scatterers of high-frequency sound, in the downwelling region beneath the surface convergence. The bands are clearly visible in sonographs. A common process of development is for them to join in pairs. The stability of the circulation pattern is examined, making a number of simplifying assumptions. In particular, we represent the Langmuir cells as linear vortices. These are subjected to small disturbances. When these are restricted to two-dimensional motions normal to the axes of the vortices, stable modes are found in part of the parameter range in which the windrow separation is large in comparison to an appropriate depth scale, such as the depth of the vortex core in a very deep mixed layer or the depth of the thermocline or lake when this is finite. These modes are destabilized to collective instabilities when three-dimensional motions are permitted. The dominant mode of instability in the parameter range in which Langmuir circulation is mostly found is, however, a pairing mode (consistent with the sonar observations), having an axial wavelength similar to the observed downwind extent of windrows. The growth rates of the instability agree favorably with those expected from observations. Further study is appropriate in view of the possible importance of this instability as a mechanism for dispersion of floating material or diffusion of soluble matter in the sea.