Reduction of mean-square advection in turbulent passive scalar mixing

TL;DR

This paper demonstrates through simulations and theoretical analysis that the variance of the coupling term in turbulent passive scalar advection is reduced compared to the assumption of independence, indicating a depression of nonlinearity.

Contribution

It provides numerical evidence and theoretical support for the reduction of mean-square advection in turbulent passive scalar mixing, extending understanding of turbulence behavior.

Findings

Variance of coupling term is smaller than independent case

Depletion effect is consistent with Kraichnan's closure theories

Depletion is approximately constant in the inertial-convective range

Abstract

Direct numerical simulation data show that the variance of the coupling term in passive scalar advection by a random velocity field is smaller than it would be if the velocity and scalar fields were statistically independent. This effect is analogous to the "depression of nonlinearity" in hydrodynamic turbulence. We show that the trends observed in the numerical data are qualitatively consistent with the predictions of closure theories related to Kraichnan's direct interaction approximation. The phenomenon is demonstrated over a range of Prandtl numbers. In the inertial-convective range the depletion is approximately constant with respect to wavenumber. The effect is weaker in the Batchelor range.