Using computational and analytical methods, we investigate the viscous and inviscid forms of the Strato-Rotational Instability (SRI) for the stratified Taylor-Couette system.
We use an eigenfunction solver to find instability modes. We are able to vary the stratification, radius ratio η and rotation-rate ratio µ, and optimise the Reynolds number and relevant wavenumbers.
We investigate the viscous and inviscid stability limits, extending the range of instability compared to prior results. Our results are consistent with the findings of Yavneh et al. [2001], Shalybkov and Rüdiger [2005], Le Bars and Le Gal [2007], Rüdiger and Shalybkov [2009], and Ibanez et al. [2016].
Building upon the results of Park and Billant [2013], we demonstrate that the µ < 1 inviscid system is unconditionally unstable if the buoyancy frequency is more than twice the inner cylinder rotation rate. For any given weaker stratification, we provide sufficient conditions for instability upon η and µ.
We explore the structure of the SRI’s critical mode throughout the [η, µ]-parameter space, for fixed stratification. The considerable variation in structural appearance suggests that various instability mechanisms exist. We also find closed domain loops, for which the SRI becomes unstable for only a finite range of Reynolds numbers. This phenomenon is associated with a discontinuous change in the critical mode within the [η, µ]-parameter space. We find considerable differences between the viscous and inviscid systems, including a region of the parameter space which for weak stratifications is only unstable in the presence of viscosity.
For the SRI to persist as a critical mode in the narrow-gap limit, we show that a near-solid-body-rotation limit is also necessary. This leads to the rotating stratified shear flow system described by Yavneh et al. [2001] for inviscid flows.
