Dependence of a passive scalar in decaying isotropic turbulence on the Reynolds and Schmidt numbers using the EDQNM model

Direct numerical simulations of decaying isotropic turbulence with a passive scalar at different Schmidt numbers show that scaling on Kolmogorov and Batchelor variables provides a reasonable collapse at large wavenumbers of the energy and scalar spectra as well as the energy and scalar transfer functions. There appears to be an approach to a k(-1) viscous-convective range at small R. and for Sc not much larger than 1. To gain some information at larger R-lambda (= 200) and Sc (>1), EDQNM ( eddy damped quasi-normal Markovian) simulations are used, after validation, at small R-lambda (= 200) and Sc (= 1, 3), against the DNS. The EDQNM model reproduces, at least qualitatively, the difference between the inertial-convective and viscous-convective ranges, although the magnitudes of the corresponding power-law exponents are -1.5 and -1.1, respectively, which differ slightly from the expected asymptotic values of -5/3 and -1. The probability density function of some of the terms in the transport equation for theta(2) provides an indication of how large radius of curvature scalar gradients may be formed