Local models of small-scale dynamo action

Coherent structures in turbulent flows consisting of vorticity filaments may generate small-scale magnetic fields by means of dynamo action with a mechanism similar to that known as the Herzenberg dynamo. In order to analyse the consequences of this assumption for the properties of the resulting magnetic field, we have performed numerical simulations for a Herzenberg-like model system with a prescribed flow, and determined the critical magnetic Reynolds number Hz for the dynamo. The critical value is of the order of a few hundred and is to be compared with the local magnetic Reynolds number for a pair of vortex filaments, calculated as a function of the Reynolds number of the flow by means of a scaling argument following Kolmogorov theory. This gives us fairly stringent conditions on the magnetic Prandtl number. PrM has to be large, of the order of a few hundred. The resulting magnetic field has a scale comparable with the diameter of the vorticity tubes and is thus of small-scale, compared to the integral scale of the flow