The Unsteady Taylor-Vortex Dynamo is Fast

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 letter, we investigate a system with two important attributes: realistic flow conditions and fast dynamo action (operational for Rm→∞). We show that unsteady Taylor-vortex flow, a classic state observed in many laboratory experiments, gives rise to fast dynamos. By numerically integrating a Floquet system driven by periodic oscillations of Taylor vortices, we solve the kinematic dynamo problem up to Rm = 3.2×10⁶, 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.