Contrasting turbulence in stably stratified flows and thermal convection

In this paper, the properties of stably stratified turbulence (SST) and turbulent thermal convection are contrasted. A key difference between these flows is the sign of the kinetic energy feed by buoyancy, ${\mathcal{F}}_B$. For SST, ${\mathcal{F}}_B<0$ due to its stable nature; consequently, the kinetic energy flux ${\mathrm{\Pi }}_u(k)$ decreases with wavenumber $k$ that leads to a steep kinetic energy spectrum, $E_u(k)\sim k^{-11\mathrm{/}5}$. Turbulent convection is unstable, hence ${\mathcal{F}}_B>0$ that leads to an increase of ${\mathrm{\Pi }}_u(k)$ with $k$; this increase however is marginal due to relatively weak buoyancy, hence $E_u(k)\sim k^{-5\mathrm{/}3}$, similar to that in hydrodynamic turbulence. This paper also describes the conserved fluxes for the above systems.