Studies of Mean Reynolds Stress Models of Turbulent Flow

In this thesis a second order turbulence model is described which calculates the mean Reynolds stresses and dissipation rate for homogeneous and slightly inhomogeneous shear flows. The higher order terms which appear in the exact differential (transport) equations for the Reynolds stresses and dissipation rate are approximated in terms of the mean velocity gradient, Reynolds stresses and dissipation rate using some of the principles of invariant modeling. The unknown coefficients appearing in the models for the higher order terms were estimated by a systematic evaluation of the available experimental data for homogeneous turbulence. The model was used to calculate the Reynolds stresses for homogeneous shear flow, homogeneous strain and the decay of initially anisotropic turbulence. The model was further tested by calculating the mean velocity and Reynolds stresses for two inhomogeneous free shear flows, the two dimensional turbulent jet and the two dimensional wake. The governing model equations were transformed into similarity form. A calculation procedure is described for the solution of the resulting set of nonlinear ordinary differential equations. A simplified version of the mean Reynolds stress model was developed and it was also used to model the plane jet and wake.