Numerical simulations of a mixed layer in a stably stratified fluid Original Research Article

We investigate numerically the generation and evolution of a mixed layer in a stably stratified Boussinesq fluid. Momentum injection is driven by a forcing term introduced in the equations of motions. As in experimental situations 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 not cause a mean flow. Typical Reynolds numbers based on the Taylor microscale are of the order of 30⩽Reλ⩽100. At moderate Reynolds numbers, the entrainment is produced by an advection-diffusion process of the temperature field. Downwards directed jets generated by the forcing deform the isotherms and create thin vertical structure where the temperature is nearly constant. At the boundaries of these jets, typical horizontal scales are much smaller than those imposed by the external forcing with the consequence that the thermal diffusion time becomes comparable 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 temperature 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 reminiscent of the classical picture of mixing due to the interaction of vortex rings with the interface which separates the mixed from the underlying quiescent fluid. After some time, these vortices start to interact together resulting in horizontal mixing of the fluid on a time scale comparable with that observed in the moderate Reynolds case.