Meridional circulation molecular-weighted

TL;DR

This paper investigates how stable molecular weight gradients influence meridional circulation in stellar and planetary interiors, revealing their role in angular momentum transport and the importance of nonlinear effects and turbulence.

Contribution

It extends the downward control principle to compositional stratification and explores the nonlinear regimes and mixing effects in meridional circulation.

Findings

Stable compositional gradients slow circulation penetration.

Nonlinear effects enable deeper mixing of elements.

Proposes models for solar tachocline and stellar rotation profiles.

Abstract

Meridional circulation in stratified stellar/planetary interiors in the presence of stable molecular weight gradients remains poorly understood, thereby affecting angular momentum transport in evolutionary models. We extend the downward control principle of atmospheric sciences to include compositional stratification. Using a linearized analysis we show that stable compositional gradients slow down the penetration of circulation into the depths, emphasizing the importance of time-dependent solutions. However, additional effects such as horizontal turbulence or magnetic fields are needed to halt it completely. We also find limits demarcating linear and nonlinear regimes in terms of Schmidt and Rossby numbers. Nonlinear simulations exhibit compositional mixing due to meridional currents, enabling deeper penetration than otherwise. We propose slowly evolving and steady-state scenarios for the solar tachocline, and helioseismically observed heavy element abundances, while acknowledging the absence of constraints on the radial variation of the Schmidt number. In the context of stellar evolution, differential rotation profiles of solar-type main-sequence stars may follow analytical solutions extending from Banik & Menou (2024), thereby aiding further probes into magneto/hydrodynamic instabilities and outward angular momentum transport.