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Turbulent fluxes of entropy and internal energy in temperature stratified flows
(Ben-Gurion University of the Negev)
We have derived 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 shown that turbulent flux of entropy is different from the turbulent
convective flux in the equation for the mean internal energy.
This turbulent convective flux is well-known in 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 the low-Mach-number temperature stratified turbulence
and is independent of a model.
We also derived equations for the velocity-entropy correlations
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.