The instability of the ocean to Langmuir circulations

It has been proposed that Langmuir circulations arise as an instability of the equations describing the Eulerian-mean flow in bodies of water supporting surface waves and subject to an applied wind stress. In infinitely deep density-stratified water, the solution of an appropriate initial-value problem is a unidirectional, time-dependent current. The stability of this current to two-dimensional (roll) disturbances is investigated by an energy analysis and by linear theory. It is found that the energy stability estimates and linear stability limits are very close, showing that subcritical instability, if it occurs, is limited to a very narrow region in parameter space. According to the present results, conditions typically occurring in the ocean are highly unstable to the Langmuir circulation instability.