The approach to self-preservation of scalar fluctuations decay in isotropic turbulence

Abstract

An analytical study of isotropic scalar fluctuations decay in isotropic turbulence is undertaken. From a fixed-point analysis, the existence of two complete self-preserving regimes is demonstrated. One of them relates to the final period of decay whereas the other one corresponds to the decay at large Reynolds and Péclet numbers. In both cases, the scalar-to-velocity timescale ratio is constant. In the final period, its asymptotic value is determined by the values of the coefficients of velocity and scalar enstrophy destruction. At large Reynolds and Péclet numbers, it depends on the latter as well as on the values of the mixed-derivative and velocity derivative skewness coefficients. A model for the approach to full self-preservation of scalar fluctuations decay is proposed. This model accounts for non-equilibrium resulting from initial unbalanced vortex stretching. In the conditions of experiments on temperature fluctuations decay in grid-turbulence, it displays a transient regime, extending over the region of measurements, during which the decay exponent is not constant but slowly varying.