Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient

In this paper, the eddy-damped quasi-normal Markovian closure is used to study the behavior of the scalar flux spectrum in isotropic turbulence as the Reynolds number Re-lambda varies in a range between 30 and 10(7). The different contributions to the evolution equation of the scalar flux spectrum are studied. One-dimensional spectra are in good agreement with direct numerical simulation (DNS) and experiments at moderate Re-lambda. The closure shows that at high Reynolds numbers, a K-7/3 scaling is found for the scalar flux spectrum, in agreement with Lumley's prediction [Phys. Fluids 10, 855 (1967)], but enormous Re-lambda are needed before it can be clearly observed. In the range of wind tunnel experiments, the spectral exponent for the scalar flux is closer to -2 in agreement with existing measurements [Mydlarski and Warhaft, J. Fluid Mech. 358, 135 (1998)]. The results for the molecular dissipation of scalar flux are in agreement with the DNS results of Overholt and Pope [Phys. Fluids A 8, 3128 (1996)]. The large Re-lambda behavior of this quantity is also addressed.