Inertial range scaling of scalar flux spectra in uniformly sheared turbulence

A model based on two-point closure theory of turbulence is proposed and applied to study the Reynolds number dependency of the scalar flux spectra in homogeneous shear flow with a cross-stream uniform scalar gradient. For the cross-stream scalar flux, in the inertial range the spectral behavior agrees with classical predictions and measurements. The streamwise scalar flux is found to be in good agreement with the results of atmospheric measurements. However, both the model results and the atmospheric measurements disagree with classical predictions. A detailed analysis of the different terms in the evolution equation for the streamwise scalar flux spectrum shows that nonlinear contributions are governing the inertial subrange of this spectrum and that these contributions are relatively more important than for the cross-stream flux. A new expression for the scalar flux spectra is proposed. It allows us to unify the description of the components in one single expression, leading to a classical $K−7∕3$ inertial range for the cross-stream component and to a new $K−23∕9$ scaling for the streamwise component that agrees better with atmospheric measurements than the $K−3$ prediction of J. C. Wyngaard and O. R. Coté [Quart. J. R. Met. Soc. 98, 590 (1972)].