Linear and non-linear stability of a thermally stratified magnetically driven rotating flow in a cylinder

The stability of a thermally stratified liquid metal flow is considered numerically. The flow is driven by the rotating magnetic field in a cylinder heated from above and cooled from below. The stable thermal stratification turns out to destabilise the flow. This is explained by the fact that a stable stratification suppresses the secondary meridional flow, thus indirectly enhancing the primary rotation. The instability in the form of Taylor-Görtler rolls is consequently promoted. It is known from earlier studies that these rolls can be only excited by finite disturbances in the isothermal flow. A sufficiently strong thermal stratification transforms this non-linear bypass instability into a linear one reducing, thus, the critical value of the magnetic driving force. A weaker temperature gradient delays the linear instability but makes the bypass transition more likely. We quantify the non-normal and non-linear components of this transition by direct numerical simulation of the flow response to noise.
It is observed that the flow sensitivity to finite disturbances increases considerably under the action of a stable thermal stratification. The capabilities of the random forcing approach to identify disconnected coherent states in a general case are discussed.