Second moment closure modeling for rotating stably stratified turbulent shear flow

The general linear second moment closure (SMC) turbulence model is considered for flows subjected to buoyancy and rotation. Model response to external forces are analyzed with the aid of structural equilibrium analysis. A closed form equilibrium solution for the anisotropy tensor bij, dispersion tensor Kij, dimensionless scalar variance q2 /k(S/Stheta )2, and the ratio of mean to turbulent time scale epsilon/ Sk is obtained. The variable of particular interest to bifurcation analysis, epsilon/Sk is shown as a function of the parameters characterizing the body forces: O/S (the ratio of the rotation rate to the mean shear rate) for rotation and Rig (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the epsilon/Sk-O/S-Rig space. It is shown, with the use of the closed form solution, that the conventional general linear models do not have a real and stable equilibrium solution when rotational and buoyant forces of certain magnitudes are simultaneously imposed on the flow. When this occurs, time integration of the turbulence model results in a diverging solution. A new model is proposed that removes this unphysical behavior. It ensures the existence of stable, real solutions for all combinations of rotation and buoyancy.; Further improvements to the model are made through bifurcation analysis. Model constants are adjusted such that the model's bifurcation characteristics are in agreement with the physically observed onset of turbulence stabilization due to stable stratification. Experimental data and numerical simulation results for stably stratified homogeneous shear flow suggest the critical gradient Richardson number of Ricrg = 0.25, and the new model is able to predict it correctly. In connection with the bifurcation analysis of SMC models, rapid distortion theory (RDT) of turbulence is applied to rotating, stably stratified shear flow to provide the stability characteristics of such flows. It is shown that the RDT predictions are not favorable when stable stratification is imposed regardless of the presence of rotation.; The new turbulence model is tested in various channel flows where inhomogeneity effects are important. Stably stratified channel flow, spanwise rotating channel flow with passive scalar, and natural convection flow in a vertical channel are considered. When compared with the predictions of the IP model, the new model yields better results for stably stratified channel flow, comparable results for rotating channel flow, and worse results for natural convection flow.