On the behavior of the velocity-scalar cross correlation spectrum in the inertial range

Abstract

The velocity-scalar cross spectrum (or scalar flux spectrum) is generally presumed to have a K−7/3 wavenumber dependence in the inertial range, in agreement with the dimensional analysis proposed by Lumley [Phys. Fluids 10, 855 (1967)]. Such a behavior is, however, clearly not observed in experiments in which spectra closer to K−2 (or even less steep) are generally found. It is shown in the paper that dimensional analysis is compatible with a K−2 scaling if a spectral flux of the velocity-scalar cross correlation is introduced. An analysis of the different terms in the equation of the scalar flux spectrum shows that two nonlinear contributions can be identified: a transfer term and the pressure contribution. Direct numerical simulations and large eddy simulation calculations are performed to obtain spectral information about the scalar flux spectrum and to analyze some key properties of the associated nonlinear transfer and pressure terms.