Strong effect of weak diffusion on scalar turbulence at large scales

TL;DR

This paper reveals that in scalar turbulence with large scale separation, weak diffusion can significantly influence scalar correlations at unexpectedly large scales, challenging traditional assumptions.

Contribution

It demonstrates the emergence of a new large-scale range where weak diffusion strongly affects scalar correlations, especially when the velocity correlation scale is much larger than the injection scale.

Findings

Diffusivity impacts scalar correlations at large scales beyond traditional expectations.

A new large-scale range, $L \,\gg\, r \gg \frac{l^2}{r_d}$, exhibits strong diffusion effects.

Counter-intuitive influence of weak diffusion on large-scale scalar turbulence.

Abstract

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale, $L$, injection scale, $l$, and diffusive scale, $r_d$. The scales are well separated if the diffusivity is small, $r_d\ll l,L$, and one normally says that effects of diffusion are confined to smaller scales, $r\ll r_d$. However, if the velocity is single scale one finds that a weak dependence of the scalar correlations on the molecular diffusivity persists to even larger scales, e.g. $l\gg r\gg r_d$ \cite{95BCKL}. We consider the case of $L\gg l$ and report a counter-intuitive result -- the emergence of a new range of large scales, $L\gg r\gg l^2/r_d$, where the diffusivity shows a strong effect on scalar correlations.