Unsteady Taylor-vortex dynamo is fast
Journal Article
Overview
abstract
; Astrophysical and geophysical fluids commonly generate organized magnetic fields, despite having enormous magnetic Reynolds numbers; ; 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 article, we investigate a system with three important attributes: realistic flow conditions, fast dynamo action (operational for; ; ; Rm; →; ∞; ; ; ), and a subharmonic spatiotemporal structure. We show that unsteady Taylor-vortex flow, a regime observed in laboratory experiments, gives rise to fast dynamos with timescales and length scales twice those of the flow at high; ; Rm; ; . By numerically integrating a Floquet system driven by periodic oscillations of Taylor vortices, we solve the kinematic dynamo problem up to; ; ; Rm; =; 3.2; ×; ; 10; 6; ; ; ; , calculating the dynamo's growth rate as a function of Rm and streamwise wave number. 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.;
