Reversed Dynamo at Small Scales and Large Magnetic Prandtl Number

Abstract

We show that at large magnetic Prandtl numbers, the Lorentz force does work on the flow at small scales and drives fluid motions, whose energy is dissipated viscously. This situation is the opposite of that in a normal dynamo, where the flow does work against the Lorentz force. We compute the spectral conversion rates between kinetic and magnetic energies for several magnetic Prandtl numbers and show that normal (forward) dynamo action occurs on large scales over a progressively narrower range of wavenumbers as the magnetic Prandtl number is increased. At higher wavenumbers, reversed dynamo action occurs, i.e., magnetic energy is converted back into kinetic energy at small scales. We demonstrate this in both direct numerical simulations forced by volume stirring and in large eddy simulations (LESs) of solar convectively driven small-scale dynamos. Low-density plasmas such as stellar coronae tend to have large magnetic Prandtl numbers, i.e., the viscosity is large compared with the magnetic diffusivity. The regime in which viscous dissipation dominates over resistive dissipation for large magnetic Prandtl numbers was also previously found in LESs of the solar corona, i.e., our findings are a more fundamental property of MHD that is not just restricted to dynamos. Viscous energy dissipation is a consequence of positive Lorentz force work, which may partly correspond to particle acceleration in close-to-collisionless plasmas. This is, however, not modeled in the MHD approximation employed. By contrast, resistive energy dissipation on current sheets is expected to be unimportant in stellar coronae.