Numerical simulations of a mixed layer in a stably stratified fluid

We investigate numerically the generation and evolution of a mixed layer in a stably stratified Boussinesq fluid. Momentum injection is driven by a fo rcing term introduced in the equations of motions. As in experimental situa tions where the energy input is due to an oscillating grid, the forcing is localized in a thin horizontal layer at the top of the domain and it does n ot cause a mean flow. Typical Reynolds numbers based on the Taylor microsca le are of the order of 30 less than or equal to Re-lambda less than or equa l to 100. At moderate Reynolds numbers, the entrainment is produced by an advection-d iffusion process of the temperature field. Downwards directed jets generate d by the forcing deform the isotherms and create thin vertical structure wh ere the temperature is nearly constant. At the boundaries of these jets, ty pical horizontal scales are much smaller than those imposed by the external forcing with the consequence that the thermal diffusion time becomes compa rable to the dynamical one. As a result, the temperature is well mixed over a few dynamical times. This process can be described using a model of temp erature advection which yields the observed scaling law of the entrainment versus the Richardson number. At higher Reynolds numbers in 2D the jets become unstable and produce pairs of secondary vortices which propagate downwards. This process is reminisce nt of the classical picture of mixing due to the interaction of vortex ring s with the interface which separates the mixed from the underlying quiescen t fluid. After some time, these vortices start to interact together resulti ng in horizontal mixing of the fluid on a time scale comparable with that o bserved in the moderate Reynolds case. (C) 2000 Elsevier Science B.V. All r ights reserved.