Spectrum of a passive scalar in moderate Reynolds number homogeneous isotropic turbulence

For moderate Reynolds numbers, the spectral scaling exponents of both velocity [E(k)∝k−mu] and the transported passive scalar [Eθ(k)∝k−mθ] fields exhibit departures from the asymptotic prediction mu=mθ=5/3. However, at the same Reynolds number, the passive scalar spectrum for homogeneous isotropic turbulence is closer to the universal asymptotic state than the dynamic velocity field that transports it. This paper provides a possible explanation for this behavior, in the case of a gaseous mixing with Prandtl (or Schmidt) number Pr≃1. A scenario of the scalar energy transfer toward higher wavenumbers is proposed and validated using experimental data, in which the velocity field itself is actively involved via its characteristic time. A direct relationship between velocity and scalar spectra and therefore between mu and mθ is thus established.