The Effects of Radially Varying Diffusivities on Stellar Convection Zone Dynamics

TL;DR

This study investigates how different radial profiles of diffusivities affect the dynamics of solar-like convection models, revealing that while kinetic energy scaling remains consistent, heat transport and turbulence distribution are sensitive to diffusivity choices.

Contribution

It systematically examines the impact of varying radial diffusivity functions on convection models, highlighting implications for model comparison and interpretation.

Findings

Kinetic energy scales similarly across diffusivity variations.

Diffusivity form influences turbulence distribution within the convection zone.

No diffusion-free behavior observed in convective heat transport.

Abstract

Convection is ubiquitous in stellar and planetary interiors where it likely plays an integral role in the generation of magnetic fields. As the interiors of these objects remain hidden from direct observation, numerical models of convection are an important tool in the study of astrophysical dynamos. In such models, unrealistic large values of the viscous ($\nu$) and thermal ($\kappa$) diffusivity are routinely used as an ad-hoc representation of the effects of subgrid scale turbulence which is otherwise too small-scale to resolve numerically. However, the functional forms of these diffusion coefficients can vary greatly between studies, complicating efforts to compare between results and against observations. We explore this issue by considering a series of non-rotating, non-magnetic, solar-like convection models with varying radial functions for the diffusivities and differing boundary conditions. We find that the bulk kinetic energy scales similarly regardless of the diffusivity parameterization. This scaling is consistent with a free-fall scaling, wherein viscosity plays a subdominant role in the force balance. We do not, however, observe such diffusion-free behavior in the convective heat transport. Our results also indicate that the functional form adopted for the diffusion coefficients can impact the distribution of turbulence within the convective shell. These results suggest that some care should be taken when comparing solar convection models directly against helioseismic observations.