Shear free turbulent entrainment and mixing at a stable density interface

Turbulence-enhanced isopycnal mixing in a stably stratified fluid is dependent on several flow parameters, though a general dependence remains uncovered. In numerical simulations of the global ocean circulation, largely mediated by such mixing, this turbulence is subgrid and so all its mixing contribution must be modeled. A useful model problem used to understand stably stratified turbulent flows is one in which turbulence interacts with an isolated density interface without the complicating influence of background shear. The database of such flows largely consists of oscillating grid turbulence (OGT) experiments.



We ran a series of high-resolution large eddy simulations which possess the classical self-similarity of velocity decay and length scale growth reported in OGT experiments. The self-similarity is broken by the presence of a density interface, but we propose “outer” and “inner” scaling laws based on a local turbulent Froude number which collapse turbulence profiles across a large range of stratification strengths. A wave-turbulence decomposition method based on the eigenmodes of the linearized equations is employed to study turbulence in the interfacial region. The observed energy conversion path is consistent with experimental observations that, for sufficiently strong stratification, the primary entrainment mechanism is internal wave breaking and local shear instabilities whereas the large-scale turbulence acts to excite interfacial waves. The dependence of entrainment rate on flow parameters is studied and found to be proportional to a local Richardson number to the minus three-halves power, consistent with many salt-stratified OGT experiments.