Comparing velocity and passive scalar statistics in fluid turbulence at high Schmidt numbers and Reynolds numbers

TL;DR

This study compares velocity and passive scalar statistics in high Reynolds and Schmidt number turbulence, revealing persistent differences even at very high Schmidt numbers, contrary to previous suggestions of convergence.

Contribution

It extends prior research by including higher Schmidt number data up to 512, showing that velocity and scalar statistics do not converge at high Reynolds and Schmidt numbers.

Findings

Velocity and scalar statistics differ significantly at all tested parameters.

Differences do not diminish with increasing Reynolds and Schmidt numbers.

Scalar and velocity behaviors remain distinct even at very high Schmidt numbers.

Abstract

Recently, Shete et al. [Phys. Rev. Fluids 7, 024601 (2022)] explored the characteristics of passive scalars in the presence of a uniform mean gradient, mixed by stationary isotropic turbulence. They concluded that at high Reynolds and Schmidt numbers, the presence of both inertial-convective and viscous-convective ranges, renders the statistics of the scalar and velocity fluctuations to behave similarly. However, their data included Schmidt numbers of 0.1, 0.7, 1.0 and 7.0, only the last of which can (at best) be regarded as moderately high. Additionally, they do not consider already available data in the literature at substantially higher Schmidt number of up to 512. By including these data, we demonstrate here that the differences between velocity and scalar statistics show no vanishing trends with increasing Reynolds and Schmidt numbers, and essential differences remain in tact at all Reynolds and Schmidt numbers.