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Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number $\mathrm{Pr}=\nu/\kappa$, where $\nu$ is the kinematic viscosity and $\kappa$ is the thermal diffusion; in stars, $\mathrm{Pr}$ is extremely low, $\mathrm{Pr}\approx 10^{-7}$. The influence of $\mathrm{Pr}$ on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using $\mathrm{Pr}\approx1$. We systematically vary $\mathrm{Pr}$ and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower $\mathrm{Pr}$ generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in $\mathrm{Pr}$. Importantly, we find that $\mathrm{Pr}$ plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number $\mathrm{Pr}=\nu/\kappa$, where $\nu$ is the kinematic viscosity and $\kappa$ is the thermal diffusion; in stars, $\mathrm{Pr}$ is extremely low, $\mathrm{Pr}\approx 10^{-7}$. The influence of $\mathrm{Pr}$ on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using $\mathrm{Pr}\approx1$. We systematically vary $\mathrm{Pr}$ and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower $\mathrm{Pr}$ generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in $\mathrm{Pr}$. Importantly, we find that $\mathrm{Pr}$ plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

We assess the robustness of a low Mach number hydrodynamics algorithm for modeling helium shell convection on the surface of a white dwarf in the context of the sub-Chandrasekhar model for Type Ia supernovae. We use the low Mach number stellar hydrodynamics code, MAESTRO, to perform three-dimensional, spatially-adaptive simulations of convection leading up to the point of the ignition of a burning front. We show that the low Mach number hydrodynamics model provides a robust description of the system., Comment: accepted to ApJ many figures degraded in quality to save space

We assess the robustness of a low Mach number hydrodynamics algorithm for modeling helium shell convection on the surface of a white dwarf in the context of the sub-Chandrasekhar model for Type Ia supernovae. We use the low Mach number stellar hydrodynamics code, MAESTRO, to perform three-dimensional, spatially-adaptive simulations of convection leading up to the point of the ignition of a burning front. We show that the low Mach number hydrodynamics model provides a robust description of the system., Comment: accepted to ApJ many figures degraded in quality to save space