Double-diffusive instabilities of differential rotation in low Pr stellar and planetary interiors

Differentially-rotating stars and planets transport angular momentum internally due to hydrodynamic (or hydromagnetic) turbulence, whose transport rates have long been a challenge to model. Stars and planets both contain low Prandtl number fluid in their interiors, with values of Pr as low as 10^{-6} in the solar radiative interior. I will present results on the linear and nonlinear properties of hydrodynamical instabilities of differential rotation in stably-stratified radiation zones of stars and planets. In particular, I will discuss the double-diffusive Goldreich-Schubert-Fricke (GSF) instability (the low Pr version of the "McIntyre instability", described by the same dispersion relation), which is driven by a destabilising angular momentum gradient if buoyancy forces are eliminated by fast thermal (relative to viscous) diffusion. This instability can drive turbulence in low Pr stellar and planetary interiors, leading to momentum transport and thermal and chemical mixing. I will first review the properties of the axisymmetric linear instability obtained within a local Cartesian Boussinesq model describing a small portion of a star, highlighting some new results. I will then present numerical simulations of its nonlinear evolution, demonstrating that it can lead to zonal jets (angular momentum layering) and enhanced turbulent transport. In a certain limit, the GSF instability is nonlinearly and formally equivalent to the salt fingering instability, so this analogy will be highlighted to aid understanding. Finally, I will describe the influence of magnetic fields, as well as a new parameter-free theory to model its turbulent transport.