The deepening of the wind-Mixed layer

Abstract

A simple model is given that describes the response of the upper ocean to an imposed wind stress. The stress drives both mean and turbulent flow near the surface, which is taken to mix thoroughly a layer of depth h, and to erode the stably stratified fluid below. A marginal stability criterion based on a Froude number is used to close the problem, and it is suggested that the mean momentum has a strong role in the mixing process. The initial deepening is predicted to obey

where u. is the friction velocity of the imposed stress, N the ambient buoyancy frequency, and t the time.

After one-half inertial period the deepening is arrested by rotadeon at a depth h = 2^2/4 u.{(Nf)⁺

where f is the Coriolis frequency. The flow is then a “mixed Ekman” layer, with strong inertial oscillations superimposed on it. Three quarters of the mean energy of the deepening layer is found to be kinetic, and only one-quarter potential.

Heating and cooling are included in the model, but stress dominates for time-scales of a day or less. Non-uniform stratification and currents existing prior to the onset of the wind are easily included.

Agreement between the first formula above and laboratory experiments of Kato and Phillips is very satisfactory; the second formula is consistent with observations of Francis and Stommel, though a more thorough test is needed. Oceanic observations in general support the assumption of slab-like mean profiles and direct response of the fluid to local winds.