Turbulent fluxes of entropy and internal energy in temperature stratified flows

Abstract

We derive equations for the mean entropy and the mean internal energy in the low-Mach-number temperature stratified turbulence (i.e., for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by ${\mathbf{F}}_s=\overline{\rho }\overline{\mathbf{u}s}$, where $\overline{\rho }$ is the mean fluid density, $s$ are fluctuations of entropy and overbars denote averaging over an ensemble of turbulent velocity field, $\mathbf{u}$. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, ${\mathbf{F}}_c=\overline{T}\overline{\rho }\overline{\mathbf{u}s}$, of the fluid internal energy, where $\overline{T}$ is the mean fluid temperature. This turbulent convective flux is well-known in the astrophysical and geophysical literature, and it cannot be used as a turbulent flux in the equation for the mean entropy. This result is exact for low-Mach-number temperature stratified turbulence and is independent of the model used. We also derive equations for the velocity-entropy correlation, $\overline{\mathbf{u}s}$, in the limits of small and large Peclet numbers, using the quasi-linear approach and the spectral tau approximation, respectively. This study is important in view of different applications to the astrophysical and geophysical temperature stratified turbulence.

10 pages, Journal of Plasma Physics, 2015, in press

References in corpus (4)

• Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope
• Structure and Evolution of Giant Cells in Global Models of Solar Convection
• Turbulence energetics in stably stratified geophysical flows: strong and weak mixing regimes
• Magnetic fluctuations and formation of large-scale inhomogeneous magnetic structures in a turbulent convection

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