TY - JOUR

T1 - Turbulent fluxes of entropy and internal energy in temperature stratified flows

AU - Rogachevskii, I.

AU - Kleeorin, N.

N1 - Publisher Copyright: © 2015 Cambridge University Press.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - We derive equations for the mean entropy and the mean internal energy in 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 Fs=σus, where σ is the mean fluid density, s is fluctuation of entropy and overbars denote averaging over an ensemble of turbulent velocity fields, u. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, Fc=T σ us , of the fluid internal energy, where 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, us, in the limits of small and large Péclet numbers, using the quasi-linear approach and the spectral τ approximation, respectively. This study is important in view of different applications to astrophysical and geophysical temperature stratified turbulence.

AB - We derive equations for the mean entropy and the mean internal energy in 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 Fs=σus, where σ is the mean fluid density, s is fluctuation of entropy and overbars denote averaging over an ensemble of turbulent velocity fields, u. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, Fc=T σ us , of the fluid internal energy, where 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, us, in the limits of small and large Péclet numbers, using the quasi-linear approach and the spectral τ approximation, respectively. This study is important in view of different applications to astrophysical and geophysical temperature stratified turbulence.

UR - http://www.scopus.com/inward/record.url?scp=84945218456&partnerID=8YFLogxK

U2 - https://doi.org/10.1017/S0022377815000963

DO - https://doi.org/10.1017/S0022377815000963

M3 - Article

SN - 0022-3778

VL - 81

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

IS - 5

M1 - 395810504

ER -