Nonlocal expression for scalar flux in turbulent shear flow

Abstract

An exact expression for the scalar flux was derived using the Green’s function for a scalar. The nonlocal eddy diffusivity involved in the expression represents a contribution to the scalar flux from the mean scalar gradient at remote points in space and time. The direct numerical simulation of channel flow was carried out to validate the nonlocal expression. The velocity and scalar fields as well as the Green’s function were calculated in the cases of one- and two-dimensional mean scalar fields and of oscillating mean scalar field. It was shown that the nonlocal expression is accurate in all the cases. A local expression for the scalar flux was also examined to show that the local approximation is not accurate enough and that the nonlocal effect is important. Some attempts were made to model the nonlocal effect. The nonlocal diffusivity was expressed algebraically using an exponential function, the local expression was modified by adding higher-order terms, and a differential equation for the nonlocal diffusivity was proposed. It was demonstrated that the analysis with the nonlocal expression gains insight into modeling the scalar transport in turbulent shear flows.