Irreversible mixing in stably-stratified wall-bounded turbulence

Evaluating irreversible vertical turbulent mixing of momentum and density in stably-stratified turbulent flows is complex and challenging. Precise quantification of irreversible mixing is of great importance in many industrial and geophysical flows. In this work, we focus on quantifying irreversible mixing in stably-stratified turbulent channel flow. To this aim, we conduct a campaign of pseudo-spectral direct numerical simulations (DNS) of the governing equations, written under the Boussinesq approximation, for shear Reynolds number Re_τ=1000 and Re_τ=180, and shear Richardson number in the range 50 ≤ Ri_τ ≤ 300 and 25 ≤ Ri_τ ≤ 75, respectively. We quantify the irreversible flux Richardson number Ri^*_f, which is a measure for irreversible mixing, and we propose a new parameterization for Ri^*_f as a function of the gradient Richardson number, Ri_g.