Linking dissipation-induced instabilities with nonmodal growth: the case of helical magnetorotational instability

TL;DR

This paper explores how dissipation-induced instabilities in helical magnetorotational flows are closely related to nonmodal growth phenomena in hydrodynamics, revealing a fundamental connection between magnetic and fluid dynamic stability.

Contribution

It demonstrates the link between dissipation-induced instabilities and nonmodal growth in hydrodynamic systems using a local approximation for helical magnetorotational instability.

Findings

Dissipation-induced instability is connected to nonmodal hydrodynamic growth.

The stability limits are continuously connected via axial electrical current.

The behavior is analyzed through pseudospectrum and local approximation methods.

Abstract

The helical magnetorotational instability is known to work for resistive rotational flows with comparably steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear are continuously connected when some axial electrical current is allowed to flow through the rotating fluid. Using a local approximation we demonstrate that the magnetohydrodynamic behavior of this dissipation-induced instability is intimately connected with the nonmodal growth and the pseudospectrum of the underlying purely hydrodynamic problem.