Phenomenology of buoyancy-driven turbulence: recent results

TL;DR

This paper reviews recent advances in buoyancy-driven turbulence, highlighting different energy spectra and flux behaviors in stratified turbulence and Rayleigh-Bénard convection, along with models predicting key flow parameters.

Contribution

It provides a comprehensive overview of recent phenomenological and numerical results, including energy spectra, flux scaling, and models for Rayleigh-Bénard convection.

Findings

Stratified turbulence exhibits Bolgiano-Obukhov scaling with $k^{-11/5}$ spectrum.

Rayleigh-Bénard convection shows Kolmogorov's $k^{-5/3}$ spectrum with constant energy flux.

Viscous dissipation in RBC scales as Ra^{1.3}.

Abstract

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.