Instability Driven Turbulence and Angular Momentum Transport in Stratified Stellar Interiors

One of the possible stellar spin-down mechanisms is turbulent transport of angular momentum (AM) gradient, which is likely unstable. This AM gradient, however, tends to be stabilized in stratified stars. To explain the observed spin down, the stabilizing effect needs to be weakened, which can be achieved by thermal diffusion, thus reinstating the instability—an effect known as the Goldreich-Schubert-Fricke (GSF) instability. While quasi-linear models have been used to estimate AM transport driven by the GSF instability, they often assume that the most unstable linear eigenmode determines nonlinear saturation properties. However, this assumption and the model predictions are not supported by nonlinear numerical simulations. To construct higher-fidelity and more robust transport models, we analyze nonlinear energy transfer among wavenumbers and identify dominant triadic interactions. These interactions are dominated by linearly stable wavenumbers near stellar equator but by linearly unstable domain-scale wavenumbers at higher latitudes. To account for this latitude-dependent behavior, we initiate a turbulence closure model to reliably capture AM transport across a broad range of latitudes. We then extrapolate our models to estimate the long-term evolutions of the solar tachocline.