Phenomenology of buoyancy-driven turbulence: Recent results

Mahendra K. Verma, Abhishek Kumar, Ambrish Pandey

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    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.
    Original languageEnglish
    JournalNew Journal of Physics
    Volume19
    Issue number2
    Publication statusPublished - 27 Feb 2017

    Bibliographical note

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    Keywords

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

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