Impact of time-dependent non-axisymmetric velocity perturbations on dynamo action of von-K\'arm\'an-like flows

TL;DR

This study uses numerical simulations to explore how time-dependent non-axisymmetric velocity perturbations influence dynamo action in von-Kármán-like flows, revealing resonance effects and spectral exceptional points affecting magnetic field growth.

Contribution

It demonstrates the impact of azimuthally drifting flow perturbations on dynamo efficiency, identifying resonance conditions and spectral exceptional points in a von-Kármán-like flow model.

Findings

Resonance-like enhancement of growth rates when vortex drift frequency matches magnetic eigenmode drift.

Two dynamo regimes: enhanced growth and modulation of magnetic fields.

Identification of a spectral exceptional point causing eigenvalue and eigenfunction collapse.

Abstract

We have performed numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von-K\'arm\'an-like flow subject to time-dependent non-axisymmetric velocity perturbations. The numerical model is based on the setup of the French Von-K\'arm\'an-Sodium dynamo (VKS) and on the flow measurements from a model water experiment conducted at the University of Navarra in Pamplona, Spain. Our simulations show that the interactions of azimuthally drifting flow perturbations with the fundamental drift of the magnetic eigenmode (caused by the inevitable equatorial symmetry breaking of the basic flow) essentially determine the temporal behavior of the dynamo state. We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an ($m=2$) vortex-like flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth-rates and a drift of the magnetic eigenmode that is synchronized with the perturbation drift. The resonance-like enhancement of the growth-rates takes place when the vortex drift frequency roughly equals the drift frequency of the magnetic eigenmode in the unperturbed system. Outside of this small window, the field generation is hampered compared to the unperturbed case, and the field amplitude of the magnetic eigenmode is modulated with approximately twice the vortex drift frequency. The abrupt transition between the resonant regime and the modulated regime is identified as an spectral exceptional point where eigenvalues (growth-rates and frequencies) and eigenfunctions of two previously independent modes collapse.