Prandtl number dependence of rotating internally heated convection

TL;DR

This study explores how the Prandtl number influences internally heated convection in rotating and non-rotating systems, revealing its impact on stratification, heat flux, and turbulence behavior relevant to planetary and stellar interiors.

Contribution

It provides new insights into the Prandtl number's role in internal stratification and heat transport, especially under rotation, through comprehensive numerical simulations.

Findings

Global mean temperature is insensitive to Prandtl number.

Low Prandtl fluids show symmetry recovery and turbulence in stable layers.

Rotation enhances heat flux but only improves cooling efficiency for Pr ≥ 1.

Abstract

We investigate the influence of the Prandtl number ($Pr$) on penetrative internally heated convection (IHC) in both non-rotating and rotating regimes using three-dimensional direct numerical simulations. By varying $Pr$ between 0.1 and 100, we show that the global mean temperature $\langle \overline{T} \rangle$ is not very sensitive to $Pr$, and is primarily controlled by the dynamics of the unstably stratified top boundary layer. In contrast, the Prandtl number dictates the behavior of the lower, stably stratified region and affects the vertical convective heat flux $\langle \overline{wT} \rangle$. In the non-rotating case, low $Pr$ fluids exhibit a ``symmetry recovery'' where turbulent stirring agitates the stable layer, whereas high $Pr$ fluids transition toward a ``dead zone'' of suppressed fluctuations. Under rotation, we find that $\langle \overline{wT} \rangle$ is enhanced across all Prandtl numbers, though global cooling efficiency, measured by the reduction in $\langle \overline{T} \rangle$, is only improved for $Pr\ge1$ due to the emergence of Ekman pumping. These results demonstrate that while IHC shares some scaling similarities with Rayleigh-B\'enard convection at the top boundary, the internal stratification creates a unique sensitivity to $Pr$ that is critical for understanding heat transport in planetary and stellar interiors.