Mean-field effects in the Galloway–Proctor flow

The coefficients defining the mean electromotive force in a Galloway–Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the α effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourthorder approximation. In the validity range of these approximations there is an α effect but no γ effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for α and show that γ is in general nonzero. Both α and γ show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity ηt and a related quantity are given, too. Finally a result for α in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the α effect and related effects in flows that are statistical isotropic in a plane.