Scaling in internally heated convection: a unifying theory

TL;DR

This paper develops a unifying theoretical framework for turbulent internally heated convection, extending previous theories for Rayleigh-Bénard and horizontal convection, and validates it with numerical simulations.

Contribution

It introduces a comprehensive theory that generalizes existing models for different types of internally heated turbulent convection.

Findings

The theory accurately predicts mean temperature and Reynolds number.

Results are consistent with direct numerical simulations.

Provides a unified approach for various internally heated convection regimes.

Abstract

We offer a unifying theory for turbulent purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, 2001) for Rayleigh--B\'enard 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.