Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow

TL;DR

This paper investigates nonaxisymmetric instabilities in cylindrical magnetohydrodynamic Taylor-Couette flow with helical magnetic fields, analyzing stability across parameters and revealing diverse instability modes and their dynamics.

Contribution

The study derives and solves eigenvalue equations for nonaxisymmetric modes, exploring how azimuthal magnetic field profiles influence various magnetorotational and Tayler instabilities.

Findings

Identification of different instability modes with varying azimuthal wave numbers

Demonstration of how magnetic field profiles affect instability dynamics

Comparison confirming the validity of WKB analysis in the linear regime

Abstract

We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself, and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are derived and solved by spectral collocation with Chebyshev polynomials over the relevant parameter space, with the resulting instabilities examined in detail. We find that by altering the azimuthal magnetic field profiles the azimuthal magnetorotational instability, nonaxisymmetric helical magnetorotational instability, and Tayler instability yield interesting dynamics, such as different preferred mode types, and modes with azimuthal wave number $m>1$. Finally, a comparison is given to the recent WKB analysis performed by Kirillov $et$ $al$. [Kirillov, Stefani, and Fukumoto, J. Fluid Mech. 760, 591 (2014)] and its validity in the linear regime.