Compressibility effects in a turbulent transport of temperature field

TL;DR

This paper investigates how compressibility influences turbulent heat transport, revealing effects like reduced turbulent diffusivity, turbulent pumping, and fluid cooling, with distinct differences from particle and magnetic field transport.

Contribution

It introduces new expressions for turbulent diffusion of temperature in compressible turbulence and analyzes the combined effects of compressibility and turbulence inhomogeneity.

Findings

Compressibility reduces turbulent diffusivity of temperature.

Inhomogeneous turbulence causes turbulent pumping of temperature.

Compressibility leads to turbulent cooling of the fluid.

Abstract

Compressibility effects in a turbulent transport of temperature field are investigated applying the quasi-linear approach for small P\'eclet numbers and the spectral $\tau$ approach for large P\'eclet numbers. Compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature field similarly to that for particle number density and magnetic field. However, expressions for the turbulent diffusion coefficient for the mean temperature field in a compressible turbulence are different from those for the mean particle number density and the mean magnetic field. Combined effect of compressibility and inhomogeneity of turbulence causes an increase of the mean temperature in the regions with more intense velocity fluctuations due to a turbulent pumping. Formally, this effect is similar to a phenomenon of compressible turbophoresis found previously [J. Plasma Phys. {\bf 84}, 735840502 (2018)] for non-inertial particles or gaseous admixtures. Gradient of the mean fluid pressure results in an additional turbulent pumping of the mean temperature field. The latter effect is similar to turbulent barodiffusion of particles and gaseous admixtures. Compressibility of a fluid flow also causes a turbulent cooling of the surrounding fluid due to an additional sink term in the equation for the mean temperature field. There is no analog of this effect for particles.