Linear and nonlinear dynamo properties of time-dependent ABC flows

The linear and nonlinear dynamo properties of a class of periodically forced flows is considered. The forcing functions are chosen to drive, in the absence of magnetic effects (kinematic regime), a time-dependent version of the ABC flow with A= B= C= 1. The time-dependence consists of a harmonic displacement of the origin along the line x= y= z= 1 with amplitude and frequency ?. The finite-time Lyapunov exponents are computed for several values of and ?. It is found that for values of these parameters near unity chaotic streamlines occupy most of the volume. In this parameter range, and for moderate kinetic and magnetic Reynolds numbers, the basic flow is both hydrodynamically and hydromagnetically unstable. However, the dynamo instability has a higher growth rate than the hydrodynamic one, so that the nonlinear regime can be reached with negligible departures from the basic ABC flow.