Stratorotational instability in Taylor–Couette flow heated from above

Abstract

We investigate the instability and nonlinear saturation of temperature-stratified Taylor–Couette flows in a finite height cylindrical gap and calculate angular momentum transport in the nonlinear regime. The model is based on an incompressible fluid in Boussinesq approximation with a positive axial temperature gradient applied. While both ingredients, the differential rotation as well as the stratification due to the temperature gradient, are stable themselves, together the system becomes subject of the stratorotational instability and a non-axisymmetric flow pattern evolves. This flow configuration transports angular momentum outwards and will therefore be relevant for astrophysical applications. The belonging coefficient of β viscosity is of the order of unity if the results are adapted to the size of an accretion disk. The strength of the stratification, the fluid's Prandtl number and the boundary conditions applied in the simulations are well suited too for a laboratory experiment using water and a small temperature gradient around 5 K. With such a set-up the stratorotational instability and its angular momentum transport could be measured in an experiment.