The Unsteady Taylor--Vortex Dynamo is Fast

TL;DR

This study demonstrates that unsteady Taylor--vortex flow can generate fast dynamos at high magnetic Reynolds numbers, with growth rates and structures relevant to astrophysical and laboratory magnetic field generation.

Contribution

It shows that realistic unsteady Taylor--vortex flows can produce fast dynamos, extending previous idealized models to more physically relevant conditions.

Findings

Fast dynamo action occurs at high Rm with flow scales twice the vortex scale.

Dynamo growth rates increase with Rm, confirming fast dynamo behavior.

Regions of Lagrangian chaos are identified as essential for dynamo efficiency.

Abstract

Astrophysical and geophysical fluids commonly generate organized magnetic fields, despite having enormous magnetic Reynolds numbers $\rm{Rm}$ and abundant small-scale turbulence. Flow-induced dynamo action produces these fields, with the ``kinematic dynamo problem'' devoted to determining the rate at which a flow exponentially amplifies weak magnetic fields. However, previous studies on high-Rm kinematic dynamos have generated flows via imposed volumetric forcing or oscillatory boundary conditions. In this letter, we investigate a system with three important attributes: realistic flow conditions, fast dynamo action (operational for $\rm{Rm}\to\infty$), and a subharmonic spatio-temporal structure. We show that unsteady Taylor--vortex flow, a regime observed in laboratory experiments, gives rise to fast dynamos with time and length scales twice those of the flow at high $\rm{Rm}$. By numerically integrating a Floquet system driven by periodic oscillations of Taylor vortices, we solve the kinematic dynamo problem up to $\rm{Rm} = 3.2 \cdot 10^6$, calculating the dynamo's growth rate as a function of Rm and streamwise wavenumber. We find the onset of instability and compute Finite-Time Lyapunov Exponents, which identify the regions of Lagrangian chaos required for fast dynamo action. To our knowledge, unsteady Taylor--vortex flow produces the most physically motivated fast dynamo to date.