Universal Realizable Anisotropic Prestress (URAPS) Closure for the Reynolds Stress

The Reynolds-averaged Navier-Stokes (RANS-) equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds (NR-) stress and the turbulent kinetic energy.~Clearly, any solution to an NS-closure model must be a non-negative operator. This longstanding problem has recently been addressed by developing a non-negative algebraic mapping of the NR-stress into itself. Consequently, all solutions of the URAPS NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. Most significantly, unlike the class of Boussinesq closures for the NR-stress, the new theory predicts the redistribution of the turbulent kinetic energy~among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows. Furthermore, the URAPS theory also predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay.