Towards a self-consistent hydrodynamical model of the solar tachocline

TL;DR

This paper critiques the classical SZ92 hydrodynamical model of the solar tachocline, introduces a new self-consistent model based on recent stratified turbulence theories, and discusses its properties and limitations.

Contribution

It proposes a new self-consistent hydrodynamical model of the solar tachocline based on horizontal turbulent diffusion, contrasting with the assumptions of the SZ92 model.

Findings

The new model's tachocline thickness scales with the ratio of solar rotation rate to buoyancy frequency.

The model aligns with recent turbulence theories and numerical validations.

It exhibits desirable features but does not solve all issues of the SZ92 model.

Abstract

The solar tachocline is an internal boundary layer in the Sun located between the differentially-rotating convection zone and the uniformly-rotating radiative interior beneath. Spiegel and Zahn (1992) proposed the first hydrodynamical model, which here we call SZ92, arguing that the tachocline is essentially in a steady state of thermal-wind balance, angular-momentum balance, and thermal equilibrium. Angular momentum transport in their model is assumed to be dominated by strongly anisotropic turbulence, primarily horizontal owing to the strong stable stratification of the radiative interior. By contrast, the heat transport is assumed to be dominated by a predominantly vertical diffusive heat flux owing to the thinness of the tachocline. In this paper, we demonstrate that these assumptions are not consistent with the new model of stratified turbulence recently proposed by Chini et al. (2022) and Shah et al. (2024), which has been numerically validated by Garaud et al. (2024). We then propose a simple self-consistent alternative to the SZ92 model, namely, a scenario wherein angular momentum and heat transport are both dominated by horizontal turbulent diffusion. The thickness of the tachocline in the new model scales as $\Omega_\odot / N_m$, where $\Omega_\odot$ is the mean angular velocity of the Sun, and $N_m$ the buoyancy frequency in the tachocline region. We discuss other properties of the model, and show that it has several desirable features, but does not resolve some of the other well-known problems of the SZ92 model.