Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

TL;DR

This paper explores how irrotational flows in compressible fluids can lead to reduced or negative mean-field diffusivities for passive scalars and magnetic fields, revealing complex non-local and memory effects through analytical and numerical methods.

Contribution

It provides new analytical and numerical insights into mean-field diffusivities in irrotational compressible flows, highlighting phenomena like negative diffusivity and slow decay due to memory effects.

Findings

Mean-field diffusivity can be smaller than molecular diffusivity.

Decay of scalar fields can be significantly slowed by flow effects.

Memory effects cause mean-field coefficients to depend on decay rates.

Abstract

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\`eclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.