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