Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

TL;DR

This paper demonstrates a nonlinear, time-periodic magnetorotational dynamo in shear flows through direct simulations, revealing a large-scale magnetic field generation mechanism beyond traditional mean-field models.

Contribution

It provides the first exact time-periodic solution for a magnetorotational dynamo in shear flows, highlighting a nonlinear process distinct from standard dynamo theories.

Findings

Identified a nonlinear large-scale dynamo mechanism.

Showed the dynamo cycle results from combined linear and nonlinear interactions.

Provided evidence that the dynamo process is not reducible to mean-field models.

Abstract

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.