Scaling in internally heated convection: a unifying theory

Abstract

We offer a unifying theory for turbulent purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, 2001) for Rayleigh--Bénard turbulence and of Shishkina, Grossmann and Lohse (2016) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nondimensionalized, the Rayleigh--Roberts number) and the Prandtl number. The results of the theory are consistent with our direct numerical simulations.

arXiv comment15 pages, 6 figures

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Cited by in corpus (10)

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• Transition between Boundary-Limited Scaling and Mixing-Length Scaling of Turbulent Transport in Internally Heated Convection
• Bistability in radiatively heated melt ponds
• Realizing the ultimate scaling of the convection turbulence by spatially decoupling the thermal and viscous boundary layers
• Rigorous scaling laws for internally heated convection at infinite Prandtl number
• Internally heated convection with rotation: bounds on heat transport
• Internally heated and fully compressible convection: flow morphology and scaling laws
• Large-scale convective flow sustained by thermally active Lagrangian tracers
• Universal properties of penetrative turbulent Rayleigh--Bénard convection in cold water near $4^{\circ }\mathrm{C}$
• Ultimate regimes in horizontal and internally heated convection