Convection driven by internal heating

TL;DR

This paper uses numerical simulations to analyze convection driven by uniform internal heating, revealing non-monotonic heat flux asymmetry and a specific temperature scaling law at high Rayleigh numbers.

Contribution

It provides new insights into heat flux asymmetry and mean temperature scaling in internally heated convection, challenging traditional diagnostic measures.

Findings

Heat flux asymmetry is non-monotonic with Rayleigh number.

Mean temperature scales as R^{-1/5} at high R.

Proposes alternative diagnostic quantities for convection analysis.

Abstract

Two-dimensional direct numerical simulations are conducted for convection sustained by uniform internal heating in a horizontal fluid layer. Top and bottom boundary temperatures are fixed and equal. Prandtl numbers range from 0.01 to 100, and Rayleigh numbers (R) are up to 5x10^5 times the critical R at the onset of convection. The asymmetry between upward and downward heat fluxes is non-monotonic in R. In a broad high-R regime, dimensionless mean temperature scales as R^{-1/5}. We discuss the scaling of mean temperature and heat-flux-asymmetry, which we argue are better diagnostic quantities than the conventionally used top and bottom Nusselt numbers.