A Vorticity–Magnetic Field Dynamo Instability

We generalize the mean field magnetic dynamo to include local evolution ofthe mean vorticity in addition to the mean magnetic field. The coupledequations exhibit a general mean field dynamo instability that enables thetransfer of turbulent energy to the magnetic field and vorticity on largerscales. The growth of the vorticity and magnetic field both require helicalturbulence which can be supplied by an underlying global rotation. The dynamocoefficients are derived including the backreaction from the mean magneticfield to lowest order. We find that a mean vorticity field can actually seedexponential growth of mean magnetic field from only a small scale seed magneticfield, without the need for a seed mean magnetic field. The equations decouplewhen the fluctuating velocity and magnetic field cross-correlations vanish,resulting in the separate mean field magnetic and mean field vorticity dynamoequations.Comment: 7pages, 0 figs, aas2pp4.sty, ApJ