terms the transport of the magnetic fluctuations by the mean velocity. The last two nonlinear terms give the effects of the back reaction due to ambipolar drift on the magnetic fluctuations.

We note that the effects of the mean velocity and magnetic fields are generally subdominant to the effects of the fluctuating velocity and magnetic fields. First the mean fields vary in general on a scale much larger than the fluctuating fields. If one neglects the effect of velocity shear due to the mean velocity, on the fluctating field, then one can transform away the mean velocity by going to a different reference frame. The mean magnetic field, ofcourse cannot be transformed away. But we will see that, it grows at a rate much slower than the fluctuating field. So when one starts from small seed magnetic fields, for most part of the evolution, we can neglect its effects. In what follows we will drop the term involving the mean fields. Due to the above reasons, we also continue to treat the statistical properties of the magnetic fluctuations as being homogeneous and isotropic, and use $M_{ij}({\bf x}, {\bf y}, t) = M_{ij}(r,t)$ as before.

All the terms in the above 