`Return-to-Equilibrium' anisotropy model for non-equilibrium Reynolds stress closures

The `Return-to-Equilibrium' closure to the Reynolds-averaged Navier-Stokes equations is a model for the Reynolds stress anisotropy b_ij, proposed to improve prediction of flows with temporal and spatial unsteadiness. It is based on the premise that the response of turbulence to imposed rates of fluid deformation is bounded between the extremes of equilibrium behavior, when db_ij /dt = 0, and rapid distortion behavior, when |db_ij /dt| >> 0, with a model b_ij transport equation to blend the response between these extremes. The model b_ij transport equation augments existing closures for the scale equations for k or ω and ε, and algebraic models for the equilibrium behavior of b_ij, yielding non-equilibrium predictions of b_ij. It has been shown to give quite accurate predictions of primary and secondary Reynolds stress evolution in two-dimensional time-dependent flows (oscillatory and impulsively-changed shear) in stationary and rotating reference frames, and in steady flows undergoing rapid spatial contraction [Phys. Fluids 37, 015180 (2025)].