Unification theory of instabilities of visco-diffusive swirling flows

TL;DR

This paper develops a comprehensive linear instability theory for swirling flows, unifying various flow types and instability criteria, and incorporating effects of viscosity and thermal diffusion to guide future experiments and simulations.

Contribution

It introduces a universal instability criterion for swirling flows that unifies centrifugal and shear-driven instabilities, extending previous analyses to include viscosity and thermal effects.

Findings

Unified instability criterion for swirling flows

Generalizes previous stability analyses

Guides experimental and numerical investigations

Abstract

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.