Dynamics of large-scale quantities in Rayleigh-Bénard convection

Abstract

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, $U$, or the Péclet number that is applicable for arbitrary Rayleigh number $\mathrm{Ra}$ and Prandtl number $\mathrm{Pr}$. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of ${\mathrm{Ra}}^{1/2}$ to the experimentally observed scaling of nearly ${\mathrm{Ra}}^{0.3}$.

arXiv comment8 pages, 6 figures

References in corpus (11)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Thermal convection for large Prandtl numbers
• Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
• The unifying theory of scaling in thermal convection: The updated prefactors
• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Energy Spectrum of Buoyancy-Driven Turbulence
• Local boundary layer scales in turbulent Rayleigh-Benard convection
• Scaling of heat flux and energy spectrum for "very large" Prandtl number convection
• Wind and boundary layers in Rayleigh-Benard convection. I: analysis and modeling
• Field correlations and the ultimate regime of turbulent convection

Cited by in corpus (10)

• Phenomenology of buoyancy-driven turbulence: recent results
• Applicability of Taylor's hypothesis in thermally driven turbulence
• Complexity of viscous dissipation in turbulent thermal convection
• Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
• Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
• Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers
• Scaling and spatial intermittency of thermal dissipation in turbulent convection
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection
• Similarities between the structure functions of thermal convection and hydrodynamic turbulence
• Transient and steady convection in two dimensions