Scaling of mixing parameters in stationary, homogeneous, and stratified turbulence

The dependency of mixing efficiency on length scales was investigated numerically for stationary, homogeneous, and stratified turbulence. Direct numerical simulations of homogeneous, sheared, and stratified turbulence were carried out under the condition of the energy equilibrium with various combinations of energy dissipation rates, stratifications, and energy-containing scales. The Reynolds number based on the Taylor microscale was between 28 and 39. It was found from the results of the numerical simulations that mixing parameters have significant dependency on the size of computational domain, which had not been discussed in the previous studies. By scaling the mixing parameters, the flux Richardson number was expressed by a function of the overturn Froude number, which is also expressed as a function of the ratio of the integral scale to the Ozmidov scale. The present model showed relevant agreements with those predicted by experimental results. From the proposed model, it is inferred that the flux Richardson number becomes its maximum of 0.2 when the thickness of the turbulence patch is sufficiently larger than the Ozmidov scale.