The dynamics of fluids deep in stellar interiors is a subject that bears many similarities with geophysical fluid dynamics, with one crucial difference: the Prandtl number. The ratio of the kinematic viscosity to the thermal diffusivity is usually of order unity or more on Earth, but is always much smaller than one in stars. As a result, viscosity remains negligible on scales that are thermally diffusive, which opens the door to a whole new region of parameter space, namely the turbulent low Péclet number regime (where the Péclet number is the product of the Prandtl number and the Reynolds number). In this review, I focus on three instabilities that are well known in geophysical fluid dynamics, and have an important role to play in stellar evolution, namely convection, stratified shear instabilities, and double-diffusive convection. I present what is known of their behavior at low Prandtl number, highlighting the differences with their moderate and high Prandtl number counterparts.

Invited review published in Physical Review Fluids