The Role of Return-to-Isotropy in Wall-Bounded Flows with Buoyancy

The workings of how buoyancy modifies turbulence statistics and the turbulent structure in stationary and planar homogeneous wall-bounded flows, such as the atmospheric boundary layer (ABL), continues to be a topic with various open fundamental questions and multiple pressing applied needs. Under neutral conditions, turbulence is produced through shear in the streamwise component and redistributed to the cross-stream and vertical components by pressure strain interactions (the so-called return to isotropy or redistribution terms in the variance equations). When buoyancy is present, it also generates or destroys turbulent kinetic energy in the vertical component. The various components mainly interact through the energy redistribution terms, and it is thus reasonable to hypothesize that any changes induced by buoyancy must be communicated by these terms to the horizontal directions.

In this talk, a reduced model with no tunable constants that connects the budgets of the three velocity variance components and captures how the redistribution terms vary with the flux Richardson number Ri_f is proposed. The model is first tested against large eddy and direct numerical simulations, then it is used to inquire about how turbulence transitions between different regimes as the Richardson number varies. The model is able to explain key topological changes in eddy structure with flux Richardson numbers at Ri_f ≈ –2, –1, –0.5, and +0.25, as well as the potential for ‘self-preservation’ of turbulence at large positive gradient Richardson numbers.