A NUMERICAL INVESTIGATION OF CONFINED TURBULENT SHEAR FLOWS

The first objective of this work is to pre~ent a new derivation of the method of coarse graining yor the computation of turbulent flows; one which strengthens and clarifies its theoretical foundation.Secondly, we show by the application of this method to the study of the turbul~nt flow in a channel and behind a piston in compressive motion that a promising start has been made toward acquiring the ability to predict the mean properties of turbulent flows.The work presented here is primarily concerned with two dimensional flow.The principal improvement in the method of coarse graining consists of the establishment of a new general law of turbulent diffusion which applies to any scalar that is passively convected in a turbulent flow.The law is in the form of an expansion in roughly the Lagrangian integral time scale.The transport law is used to derive a closed set of equations for the mean vorticity and mean squared fluctuating vorticity.Other innovations include a more precise accounting of the effects of the local turbulence on the velocity moments and the use of an explicit equation for mean squared fluctuating vorticity instead of mean square.dvorticity.