Stratified turbulence in the solar tachocline

The solar tachocline is an internal boundary layer in the Sun located between the differentially-rotating convection zone and the uniformly-rotating radiative zone. Spiegel and Zahn (1992) proposed the first hydrodynamical model of the tachocline, arguing that it is 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, primarily horizontal turbulence, owing to the strong stratification of that region. Meanwhile heat transport is assumed to be dominated by a predominantly vertical diffusive heat flux. 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 was numerically validated by Garaud et al. 2024. Instead, we show that the thermal equilibrium in this type of tachocline model must also involve anisotropic horizontal heat transport by the turbulent flows. We therefore propose a alternative model of the tachocline, demonstrate that it is self-consistent, and discuss its properties.