Minimal perturbation flows that trigger mean field dynamos in shear flows

Using a variational optimization method we find the smallest flow perturbations that can trigger kinematic dynamo action in Kolmogorov flow. In comparison to previous work, a second-order mean field dynamo model is used to track down the optimal dynamos in the high magnetic Reynolds number limit (R_m). The magnitude of minimal perturbation flows decays inversely proportional to the magnetic Reynolds number. We reveal the asymptotic high-R_m structure of the optimal flow perturbation and the magnetic eigenmode. We identify the optimal dynamo as of α-Ω type, with magnetic fluctuations that localize on a critical layer.