Dynamo action in flows with cat’s eyes

This paper considers dynamo action in steady fluid flows having a cat’s eye stream line topol-ogy. The flows considered are two-dimensional, depending on x and y only, but have all three components of velocity and hence can act as kinematic dynamos. The limit of large magnetic Reynolds number (R) is considered and the numerical results are presented for the different types of magnetic mode that can be amplified. In particular, a new class of modes, which are termed cat’s eye modes, is identified. These modes consist of sheets of field that lie along the separatrices and hyperbolic points that define a single row of as cat’s eyes. They have growth rates that fall off very slowly with a large R, and their wavenumber k in the z direction scales approximately as ffiffiffiffi R p. The fluid flow amplifies these magnetic fields by a variant of the stretch–fold–shear mechanism, acting in a steady flow