The proposal is aimed at obtaining a unified treatment of turbulent mixing and of turbulent transfer to a wall of molecular species, and of spherical particles. Theory in this area has not advanced significantly over the past forty years. However, the recent availability of direct numerical simulations opens the possibility of making considerable progress. A main objective of this proposal is to exploit this opportunity. Results on the simultaneous three-dimensional time-dependent velocity and temperature fields will be obtained for a wide range of Prandtl numbers for turbulent flow in a channel and for turbulent Couette flow. Present theories will be evaluated. However, special emphasis will be placed on the relation of the structure of the temperature field to the structure of the velocity field and on how turbulent transport is modified by molecular transport. Lagrangian methods will be explored as a means to obtained better physical understanding. The temperature field is viewed as resulting from a distribution of wall sources. The exploitation of this approach has been opened up because of the possibility of studying, on the computer, the behavior of wall sources. The transport of spherical particles differs from transport of molecular species because of extraneous contributions to transport by gravity, turbophoresis and lift. These effects will be studied both in computer and in laboratory experiments. Particular attention will be given to obtaining much needed information about inertial free flight to the wall. We will also continue recent work in which we exploit Lagrangian methods to analyze sediment transport.
