Stress-driven mixed layer in a stably stratified fluid

We investigate numerically a two-dimensional flow where a shear layer is forced at the top of a linearly stratified fluid. As a consequence of the mechanical forcing, a statistically steady stress is exerted on the underlying fluid. The downwards transfer of momentum and buoyancy, characterized by the deepening of a mixed layer, is studied for three different values of the initial Brunt-Vaisala frequency N*. We show that the flow reaches an asymptotic stage where the temporal evolution of the mixed layer becomes statistically self-similar. The spatial scaling factor is the mixed layer depth il(t) whose evolution is proportional to u*/N*root tN*, where u* is a velocity associated to the stress tau = rho(0)u*(2). These results are compared to previous theoretical and empirical models which have been proposed to describe the deepening of the oceanic mixed layer under the action of a wind stress. Astrophysical applications are also mentioned.