  The diffusion of uni-directional magnetic fields by two dimensional turbulent
flows in a weakly ionized gas is studied. The fields here are orthogonal to the
plane of fluid motion. This simple model arises in the context of the decay of
the mean magnetic flux to mass ratio in the interstellar medium. When ions are
strongly coupled to neutrals, the transport of a large--scale magnetic field is
driven by both turbulent mixing and nonlinear, ambipolar drift. Using a
standard homogeneous and Gaussian statistical model for turbulence, we show
rigorously that a large-scale magnetic field can decay on at most turbulent
mixing time scales when the field and neutral flow are strongly coupled. There
is no enhancement of the decay rate by ambipolar diffusion. These results
extend the Zeldovich theorem to encompass the regime of two dimensional flows
and orthogonal magnetic fields, recently considered by Zweibel (2002). The
limitation of the strong coupling approximation and its implications are
discussed.
