Oleg Kirillov (Northumbria) – Local instabilities of visco-diffusive swirling flows with a radial heating

Swirling flows induced by the combination of rotation and shear in orthogonal directions are ubiquitous in various natural phenomena, such as tornadoes and tropical cyclones, meandering rivers, vortex rings with swirl, and geophysical and astrophysical flows. These flows also occur in trailing vortices of aircraft wingtips and in branching junctions of everyday piping systems and physiological flows, where identifying instabilities that lead to vortex breakdown is of paramount importance. Swirling flows are present in industrial processes, such as filtration or purification of wastewater, isotope separation through centrifugation, and oil-drilling systems. They are also characteristic of convective flows with rotation, associated with cooling or lubrication of rotating machinery, crystal growth, and solidification of metals.

From a hydrodynamic perspective, the base state of a swirling flow has azimuthal and axial velocity components in either open or confined geometries. The open flow configuration is typical of swirling jets in natural phenomena, while the confined one is more common in engineering. A convenient setup to study swirling flows, both theoretically and experimentally, confines the fluid in a cylindrical annulus with differentially rotating cylinders, creating the classical circular Couette-Taylor flow. The axial component in this setup can be induced by an external pressure gradient, as in Spiral Poiseuille flow (SPF), by sliding inner cylinder, as in Spiral Couette flow (SCF), or by a radial temperature gradient, as in baroclinic Couette flow (BCF).

In this talk I present a universal theory of instabilities in swirling flows, occurring in both natural settings and industrial applications. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows and baroclinic flows driven by radial temperature gradients and natural gravity in rotating fluids. By employing short-wavelength local analysis, the theory generalizes previous findings from numerical simulations and linear stability analyses of specific swirling flows, such as spiral Couette flow, spiral Poiseuille flow, and baroclinic Couette flow. A general criterion, extending and unifying existing criteria for instability to both centrifugal and shear-driven perturbations in swirling flows is derived, taking into account viscosity and thermal diffusion and guiding experimental and numerical investigations in the otherwise inaccessible parameter regimes.