Abstract

Swirling flows, arising from the interaction of rotation and shear, are central to many engineering and geophysical systems, ranging from combustion to screw-type dynamos in magnetohydrodynamics. Even when Rayleigh-stable, such flows can exhibit ring-mode instabilities, first identified by Leibovich and Stewartson in the aerodynamical context of trailing vortices, which are highly localised in radius and play an important role in spiral-type vortex breakdown. Owing to their local character, these instabilities are naturally analysed using short-wavelength, WKB -based methods such as the Lifschitz–Hameiri geometrical-optics approach. In this talk, I examine the stability of visco-thermodiffusive swirling flows in annular geometries with differentially rotating and differentially heated coaxial cylinders. Using a modified Lifschitz–Hameiri framework, I analyse localised ring modes in spiral Couette and spiral Poiseuille flows, with and without a radial temperature gradient, as well as in baroclinic Couette flow. This allows the classical Leibovich–Stewartson criterion to be extended to non-isothermal, viscous, thermally diffusive flows. A central result is the discovery of a visco-diffusive oscillatory instability of McIntyre type, absent in the inviscid or isothermal limits. The results clarify how viscosity and thermal diffusion modify local instability mechanisms in swirling flows and provide new insight into the dynamics of non-isothermal Couette–Taylor systems.