Phenomenology of buoyancy-driven turbulence: recent results

Abstract

In this paper, we describe the recent developments in the field of buoyancy-driven turbulence with a focus on energy spectrum and flux. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum ${E}_{u}(k)\sim {k}^{-11/5}$ and the kinetic energy flux ${{\rm{\Pi }}}_{u}(k)\sim {k}^{-4/5}$ , which is called Bolgiano-Obukhov scaling. However, for Prandtl number near unity, the energy flux for the three-dimensional Rayleigh–Bénard convection (RBC) is approximately constant in the inertial range that results in Kolmorogorv’s spectrum ( ${E}_{u}(k)\sim {k}^{-5/3}$ ) for the kinetic energy. The phenomenology of RBC should apply to other flows where the buoyancy feeds the kinetic energy, e.g. bubbly turbulence and fully-developed Rayleigh Taylor instability. This paper also covers several models that predict the Reynolds and Nusselt numbers of RBC. Recent works show that the viscous dissipation rate of RBC scales as $\sim {\mathrm{Ra}}^{1.3}$ , where $\mathrm{Ra}$ is the Rayleigh number.

Keywords

• buoyancy-driven flows
• Rayleigh–Benard convection
• stably-stratified turbulence
• thermal convection
• thermally-driven turbulence