Meridional circulation molecular-weighted

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.