Scaling in internally heated convection: a unifying theory

Wang, Qi; Lohse, Detlef; Shishkina, Olga

doi:10.1029/2020GL091198

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Scaling in internally heated convection: a unifying theory

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Lohse, Detlef
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Shishkina, Olga
Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Wang, Q., Lohse, D., & Shishkina, O. (2020). Scaling in internally heated convection: a unifying theory. Geophysical Research Letters, 48: e2020GL091198. doi:10.1029/2020GL091198.

Cite as: https://hdl.handle.net/21.11116/0000-0007-E37A-0

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 of the Boussinesq equations.