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High 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}