A VORTICITY MAGNETIC-FIELD DYNAMO INSTABILITY

We generalize the mean field magnetic dynamo to include local evolutio n of the mean vorticity in addition to the mean magnetic field. The co upled equations exhibit a general mean field dynamo instability that e nables the transfer of turbulent energy to the magnetic field and vort icity on larger scales. The growth of vorticity and magnetic field bot h require helical turbulence, and the helicity can be supplied by an u nderlying global rotation. The dynamo coefficients are derived, includ ing the back-reaction from the mean magnetic field to lowest order. We find that a mean vorticity field can actually seed exponential growth of a mean magnetic field from only a small-scale seed magnetic field, without the need for a seed mean magnetic field. The equations decoup le when the fluctuating velocity and magnetic field cross-correlations vanish, resulting in the separate mean field magnetic and mean field vorticity dynamo equations.