Spectra of velocity and temperature fluctuations with constant entropy flux of fully developed free-convective turbulence

It is shown that the frequency-temperature spectrum recently observed by Wu et al. in developed convective turbulence, ${\mathit{F}}_{\mathit{T}\mathit{T}}$(ω)∝${\mathrm{\omega }}^{\mathrm{-}1.4}$, follows from the condition that the entropy flux in $ k — space is constant, just as the Kolmogorov-Obukhov spectrum of barotropic turbulence, ${\mathit{F}}_{\mathit{V}\mathit{V}}$(k)≃(ɛ/ρ${)}^{2/3}$ ${\mathit{k}}^{\mathrm{-}11/3}$, follows from the condition kinetic-energy flux ɛ(k)=ɛ. On the contrary, for convective turbulence ɛ(k) changes as ${\mathit{k}}^{\mathrm{-}4/5}$ because of conversion of kinetic energy into a potential energy, which leads to a stronger k dependence of the double velocity moment [${\mathit{F}}_{\mathit{V}\mathit{V}}$(k)∝${\mathit{k}}^{\mathrm{-}21/5}$] than that for barotropic turbulence.