Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows

TL;DR

This paper rigorously analyzes the eigenvalue distributions of linearized operators in ideal hydromagnetic Couette-Taylor flows, revealing a paradoxical transition to instability that differs from classical hydrodynamic criteria, especially as magnetic effects vanish.

Contribution

It provides a spectral analysis showing the discontinuous change in stability criteria in magnetic flows, highlighting the Velikhov-Chandrasekhar paradox.

Findings

Eigenvalue distributions are rigorously derived.

Transition to instability is discontinuous at zero magnetic field.

The Velikhov-Chandrasekhar paradox is confirmed mathematically.

Abstract

By methods of modern spectral analysis, we rigorously find distributions of eigenvalues of linearized operators associated with an ideal hydromagnetic Couette-Taylor flow. Transition to instability in the limit of vanishing magnetic field has a discontinuous change compared to the Rayleigh stability criterion for hydrodynamical flows, which is known as the Velikhov-Chandrasekhar paradox.