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We have performed numerical simulations of the kinematic induction equationin order to examine the dynamo efficiency of an axisymmetricvon-K\'arm\'an-like flow subject to time-dependent non-axisymmetric velocityperturbations. The numerical model is based on the setup of the FrenchVon-K\'arm\'an-Sodium dynamo (VKS) and on the flow measurements from a modelwater experiment conducted at the University of Navarra in Pamplona, Spain. Oursimulations show that the interactions of azimuthally drifting flowperturbations with the fundamental drift of the magnetic eigenmode (caused bythe inevitable equatorial symmetry breaking of the basic flow) essentiallydetermine the temporal behavior of the dynamo state. We find two distinctregimes of dynamo action that depend on the (prescribed) drift frequency of an($m=2$) vortex-like flow perturbation. For comparatively slowly driftingvortices we observe a narrow window with enhanced growth-rates and a drift ofthe magnetic eigenmode that is synchronized with the perturbation drift. Theresonance-like enhancement of the growth-rates takes place when the vortexdrift frequency roughly equals the drift frequency of the magnetic eigenmode inthe unperturbed system. Outside of this small window, the field generation ishampered compared to the unperturbed case, and the field amplitude of themagnetic eigenmode is modulated with approximately twice the vortex driftfrequency. The abrupt transition between the resonant regime and the modulatedregime is identified as an spectral exceptional point where eigenvalues(growth-rates and frequencies) and eigenfunctions of two previously independentmodes collapse.

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