Vortex tube models for turbulent dynamo action

The possibility of dynamo action resulting from a pair of elongated vortex structures immersed in an electrically conducting fluid is investigated. For elongated vortex structures, the critical magnetic Reynolds number for dynamo action is about half that for the spherical rotors that have been studied previously. When applied to Kolmogorov turbulence with vortex structures of scale comparable to the dissipation length, this model can explain dynamo action only when the magnetic Prandtl number (=kinematic viscosity/magnetic diffusivity) exceeds a critical value that is larger than unity. It is argued that in astrophysical bodies where this condition is not satisfied (in stellar convection zones, for example), dynamo action must instead result from motions on all scales up to the size of the region.