%ABou-Zeid, Elie%AGao, Xiang%AAnsorge, Cedrick%AKatul, Gabriel%BJournal Name: Journal of Fluid Mechanics; Journal Volume: 856
%D2018%I
%JJournal Name: Journal of Fluid Mechanics; Journal Volume: 856
%K
%MOSTI ID: 10086039
%PMedium: X
%TOn the role of return to isotropy in wall-bounded turbulent flows with buoyancy
%XHigh Reynolds number wall-bounded turbulent flows subject to buoyancy forces are fraught with complex dynamics originating from the interplay between shear generation of turbulence ( $S$ ) and its production or destruction by density gradients ( $B$ ). For horizontal walls, $S$ augments the energy budget of the streamwise fluctuations, while $B$ influences the energy contained in the vertical fluctuations. Yet, return to isotropy remains a tendency of such flows where pressure–strain interaction redistributes turbulent energy among all three velocity components and thus limits, but cannot fully eliminate, the anisotropy of the velocity fluctuations. A reduced model of this energy redistribution in the inertial (logarithmic) sublayer, with no tuneable constants, is introduced and tested against large eddy and direct numerical simulations under both stable ( $B<0$ ) and unstable ( $B>0$ ) conditions. The model links key transitions in turbulence statistics with flux Richardson number (at $Ri_{f}=-B/S\approx$ $-2$ , $-1$ and $-0.5$ ) to shifts in the direction of energy redistribution. Furthermore, when coupled to a linear Rotta-type closure, an extended version of the model can predict individual variance components, as well as the degree of turbulence anisotropy. The extended model indicates a regime transition under stable conditions when $Ri_{f}$ approaches $Ri_{f,max}\approx +0.21$ . Buoyant destruction $B$ increases with increasing stabilizing density gradients when $Ri_{f}