The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow

Abstract

The effect of an arbitrarily oriented mean passive scalar gradient on one-point passive scalar statistics is studied in homogeneous turbulent shear flow in the limit of rapid shearing. By neglecting the nonlinear inertial transfer to small scales an analytical solution for individual Fourier modes is obtained for the case of unity Prandtl number. This solution is used to compute the development of one-point statistics for the velocity and scalar fields in the inviscid limit. Comparisons to direct numerical simulations of the full nonlinear equations for the same flow show that in addition to describing the early time response to the imposed shear, the linear solution gives reasonable estimates of several correlation coefficients for the developed shear flow.