  Rotation measure (RM) synthesis maps of NGC 4631 show remarkable sign
reversals with distance from the minor axis in the northern halo of the galaxy
on kpc scales. To explain this new phenomenon, we solve the dynamo equations
under the assumption of scale invariance and search for rotating logarithmic
spiral solutions. Solutions for velocity fields representing accretion onto the
disk, outflow from the disk, and rotation-only in the disk are found that
produce RM with reversing signs viewed edge-on. Model RM maps are created for a
variety of input parameters using a Faraday screen and are scaled to the same
amplitude as the observational maps. Residual images are then made and compared
to find a best fit. Solutions for rotation-only, i.e. relative to a pattern
uniform rotation, did in general, not fit the observations of NGC 4631 well.
However, outflow models did provide a reasonable fit to the magnetic field. The
best results for the specific region that was modelled in the northern halo are
found with accretion. Since there is abundant evidence for both winds and
accretion in NGC 4631, this modelling technique has the potential to
distinguish between the dominant flows in galaxies.
