Phenomenology of buoyancy-driven turbulence: Recent results

In this paper, we review the recent developments in the field of buoyancy-driven turbulence. 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 $\Pi_u(k) \sim k^{-4/5}$, which is called Bolgiano-Obukhov scaling. The energy flux for the Rayleigh-B\'{e}nard convection (RBC) however 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

Intermittency in Rayleigh-Bénard convection

Experimental evidence of a transition to turbulence via intermittency is reported for a convection experiment of a high Prandtl number fluid in confined geometry. This transition is qualitatively understood in terms of a model derived from recent results on the Lorenz system.Nous présentons la première évidence expérimentale d'une transition vers la turbulence par intermittence dans une expérience de convection à nombre de Prandtl élevé et en géométrie confinée. Il est possible d'interpréter qualitativement cette transition à partir d'un modèle qui se déduit de résultats récents obtenus sur le système de Lorenz