Phenomenology of buoyancy-driven turbulence: recent results

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-Bénard 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.

References in corpus (16)

• High Reynolds number Taylor-Couette turbulence
• Rotations and cessations of the large-scale circulation in turbulent Rayleigh-Benard convection
• Energy Spectrum of Buoyancy-Driven Turbulence
• Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection
• Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Benard turbulence
• Scaling of large-scale quantities in Rayleigh-Bénard convection
• Dynamics of reorientations and reversals of large scale flow in Rayleigh-Benard convection
• Local boundary layer scales in turbulent Rayleigh-Benard convection
• A Shell Model for Buoyancy-Driven Turbulence
• Near isotropic behaviour of turbulent thermal convection
• Wind and boundary layers in Rayleigh-Benard convection. I: analysis and modeling
• Flow reversals in turbulent convection with free-slip walls
• Dynamics of reversals and condensates in 2D Kolmogorov flows
• Logarithmic Spatial Variations and Universal $f^{-1}$ Power Spectra of Temperature Fluctuations in Turbulent Rayleigh-Bénard Convection
• Dynamics of large-scale quantities in Rayleigh-Bénard convection
• Anomalous Scaling and Refined Similarity of an Active Scalar in a Model of Homogeneous Turbulent Convection

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