Scaling in Internally Heated Convection: A Unifying Theory

We offer a unifying theory for turbulent, purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, https://doi.org/10.1017/S0022112099007545; 2001, https://doi.org/10.1103/PhysRevLett.86.3316) for Rayleigh-Benard turbulence and of Shishkina et al. (2016, https://doi.org/10.1002/2015GL067003) 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. Plain Language Summary Internally heated convection (IHC), that is, convective fluid motions driven by the internal heat generation, is an omnipresent phenomenon in many geo- and astrophysical convective flows. An important question for IHC is how the mean temperature and the global flow strength depend on the internal heating rate and the operating fluid. In this work, we offer a unifying theory to address this question. The results of the theory agree well with our direct numerical simulations.

Automated summary

A unified theory for turbulent, purely internally heated convection is proposed, providing insights into the dependence of mean temperature and global flow strength on internal heating rate and fluid properties. The theory's results are consistent with direct numerical simulations of the Boussinesq equations.