Unification theory of instabilities of visco-diffusive swirling flows

A universal theory of linear instabilities in swirling flows, occurring in both natural settings and industrial applications, is formulated. 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.