Compressible turbulent convection: The role of temperature-dependent thermal conductivity and dynamic viscosity

TL;DR

This study investigates how temperature-dependent thermal conductivity and viscosity influence compressible turbulent convection, revealing systematic quantitative effects on flow properties and heat/momentum transfer without altering qualitative flow behavior.

Contribution

It provides the first detailed analysis of the impact of temperature-dependent material properties on fully compressible turbulent convection beyond the anelastic approximation.

Findings

Quantitative changes in flow statistics due to material property dependence.

Enhanced momentum transfer with increasing temperature power law exponent in weak stratification.

Reduced heat transfer with increasing temperature power law exponent in strong stratification.

Abstract

The impact of variable material properties, such as temperature-dependent thermal conductivity and dynamical viscosity, on the dynamics of a fully compressible turbulent convection flow beyond the anelastic limit are studied in the present work by two series of three-dimensional direct numerical simulations in a layer of aspect ratio 4 with periodic boundary conditions in both horizontal directions. One simulation series is for a weakly stratified adiabatic background, one for a strongly stratified one. The Rayleigh number is $10^5$ and the Prandtl number is 0.7 throughout this study. The temperature dependence of material parameters is imposed as a power law with an exponent $\beta$. It generates a superadiabaticity $\varepsilon(z)$ that varies across the convection layer. Central statistical quantities of the flow, such as the mean superadiabatic temperature, temperature and density fluctuations, or turbulent Mach numbers are compared in the form of horizontal plane-time averaged profiles. It is found that the additional material parameter dependence causes systematic quantitative changes of all these quantities, but no qualitative ones. A growing temperature power law exponent $\beta$ also enhances the turbulent momentum transfer in the weak stratification case by 40\%, it reduces the turbulent heat transfer by up to 50\% in the strong stratification case.