### Abstract

Theoreticians often study nonlinear dynamos by postulating a specific force field designed to produce a flow which is known to give rise to an effective kinematic dynamo. The subsequent evolution is then followed numerically to determine how the dynamo equilibrates. The most studied example is the (1,1,1) ABC flow, with the supplied forcing proportional to the inverse kinetic Reynolds number. In this case, scaling arguments can be adduced which give very pessimistic estimates for the high Reynolds number performance of the dynamo. Recently Archontis (PhD thesis, 2000) found an interesting example of a dynamo where the performance is far superior, with approximately equal scaled magnetic and velocity fields which are very close to (sin z,sin x,sin y) when the kinetic and magnetic Reynolds numbers are large. Numerical results will be described which attempt to show how and why this and some similar dynamos work so well, and whether such behaviour can be expected in real astrophysical objects.