Velocity Amplitudes in Global Convection Simulations: The Role of the Prandtl Number and Near-Surface Driving

TL;DR

This study investigates how the Prandtl number and near-surface driving influence velocity amplitudes in global solar convection simulations, revealing that higher Prandtl numbers can limit flow speeds, with implications for modeling solar dynamics.

Contribution

It demonstrates that increasing the Prandtl number decreases velocity amplitudes in simulations, contrasting with fixed Prandtl cases, and suggests high Prandtl regimes may better represent solar convection.

Findings

Velocity amplitude increases with fixed Prandtl number, then saturates.

Velocity amplitude decreases with increasing Prandtl number when viscosity is fixed.

High Prandtl number regimes could limit flow speeds in solar convection models.

Abstract

Several lines of evidence suggest that the velocity amplitude in global simulations of solar convection, U, may be systematically over-estimated. Motivated by these recent results, we explore the factors that determine U and we consider how these might scale to solar parameter regimes. To this end, we decrease the thermal diffusivity $\kappa$ along two paths in parameter space. If the kinematic viscosity $\nu$ is decreased proportionally with $\kappa$ (fixing the Prandtl number $P_r = \nu/\kappa$), we find that U increases but asymptotes toward a constant value, as found by Featherstone & Hindman (2016). However, if $\nu$ is held fixed while decreasing $\kappa$ (increasing $P_r$), we find that U systematically decreases. We attribute this to an enhancement of the thermal content of downflow plumes, which allows them to carry the solar luminosity with slower flow speeds. We contrast this with the case of Rayleigh-Benard convection which is not subject to this luminosity constraint. This dramatic difference in behavior for the two paths in parameter space (fixed $P_r$ or fixed $\nu$) persists whether the heat transport by unresolved, near-surface convection is modeled as a thermal conduction or as a fixed flux. The results suggest that if solar convection can operate in a high-$P_r$ regime, then this might effectively limit the velocity amplitude. Small-scale magnetism is a possible source of enhanced viscosity that may serve to achieve this high-$P_r$ regime.