On the Stability of a Rotating Cylindrical Shear Flow: Consequences for Differentially Rotating Vortical Structures

We propose a mechanism for generation of vorticity in a rotating cylindrical shear flow and predict the effect of background rotation through three-dimensional linear stability analysis and direct numerical simulations (DNSs). Our linear theory predicts a positive feedback of angular momentum for moderate rotation rates that agree well with early time evolution of DNSs with weak rotation. These runs show the growth of low azimuthal wavenumber modes of instability at early times with subsequent onset of centrifugal instabilities that arrests the initial spin-up of the core. For stronger background rotation, we observe the emergence of helical modes of instability from very early times which drain angular momentum out of the vortex core. We discuss a possible caveat of the DNS results with regards to the choice of our domain size that appears to influence our prediction for low Rossby numbers and its implications for understanding the emergence and growth of large-scale vortices as commonly observed in DNSs of turbulent convection as well as natural flows in astrophysical and geophysical contexts.