Computational Modeling of Turbulent Transport

A rational closure technique is presented for the first and second moment-equations in a stratified, contaminated turbulent flow, Following the application of high Reynolds/Peclet number approximations, remaining third moments are expanded about the isotropic, homogeneous state. The stratified, uncontaminated case reduces to seventeen equations in seventeen unknowns. Other authors have suggested some of the terms generated, but Some have been using the wrong terms, or the right terms for the wrong reasons. The approximation is kinetic-theoretic (turbulence/mean motion scales assumed small, and turbulence nearly in equilibrium) and results in a relaxation time, and in generalized gradient transport forms; however, gradients of one quantity can produce fluxes of another. The model relates the time scale for return to isotropy to the Lagrangian integral time scale (reducing to K-theory in a homogeneous parallel flow with orthogonal temperature gradient). Some coefficients are estimated, and preliminary computations arc presented of the unstratified 2-D turbulent wake; only component energies near the centerline are not well reproduced, probably due to the omission of a term with which temporary computational difficulties were being experienced. Stratified, contaminated 3-D calculations appear to be practical