Scaling of large-scale quantities in Rayleigh-Bénard convection

Abstract

We derive a formula for the Péclet number ($\mathrm{Pe}$) by estimating the relative strengths of various terms of the momentum equation. Using direct numerical simulations in three dimensions we show that in the turbulent regime, the fluid acceleration is dominated by the pressure gradient, with relatively small contributions arising from the buoyancy and the viscous term, in the viscous regime, acceleration is very small due to a balance between the buoyancy and the viscous term. Our formula for $\mathrm{Pe}$ describes the past experiments and numerical data quite well. We also show that the ratio of the nonlinear term and the viscous term is $\mathrm{Re}{\mathrm{Ra}}^{-0.14}$, where $\mathrm{Re}$ and $\mathrm{Ra}$ are Reynolds and Rayleigh numbers respectively, and that the viscous dissipation rate ${\epsilon }_u=(U^3/d){\mathrm{Ra}}^{-0.21}$, where $U$ is the root mean square velocity and $d$ is the distance between the two horizontal plates. The aforementioned decrease in nonlinearity compared to free turbulence arises due to the wall effects.

arXiv comment35 pages, 15 figures

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• Thermal boundary layer structure in low-Prandtl-number turbulent convection
• Convective mesoscale turbulence at very low Prandtl numbers
• Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
• Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
• Non-Boussinesq low-Prandtl number convection with a temperature-dependent thermal diffusivity
• Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection
• Scaling and spatial intermittency of thermal dissipation in turbulent convection
• Similarity model for corner roll in turbulent Rayleigh-Benard convection
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• Similarities between characteristics of convective turbulence in confined and extended domains
• Similarities between the structure functions of thermal convection and hydrodynamic turbulence
• Contrasting turbulence in stably stratified flows and thermal convection
• Transient and steady convection in two dimensions
• Turbulent convection in rotating slender cells
• Influence of plume activity on thermal convection in a rectangular cell