Statistical Approach to Inhomogeneous Trubulence with Unidirectional Mean Flow: Evaluation of Reynolds Stress

Statistical analysis is made of the inhomogeneous turbulence with unidirectional mean flow in infinite fluid. The velocity is assumed to depend on the coordinate normal to the flow. Considering that the space variation of the mean flow is small compared with that of the fluctuating one, two space scales corresponding to mean and fluctuating flows are introduced into the Navier-Stokes equations. The direct-interaction approximation is applied to the equation thus found, and Reynolds stress is evaluated. Results obtained are applied to the calculation of grid-scale Reynolds stress used frequently in a numerical simulation of turbulent flows.