  A flow of electrically conducting fluid in the presence of a steady magnetic
field has a tendency to become quasi two-dimensional, i.e. uniform in the
direction of the magnetic field, except in thin so-called Hartmann boundary
layers. The condition for this tendency is that of a strong magnetic field,
corresponding to large values of the dimensionless Hartmann number (Ha >> 1).
This is analogous to the case of low Ekman number rotating flows, with Ekman
layers replacing Hartmann layers. This has been at the origin of the
homogeneous model for flows in a rotating frame of reference, with its rich
structure: geostrophic contours and shear layers of Stewartson, Munk and
Stommel. In magnetohydrodynamics, the characteristic surfaces introduced by
Kulikovskii play a role similar to the role of the geostrophic contours.
However, a general theory for quasi two-dimensional magnetohydrodynamics is
lacking. In this paper, a model is proposed which provides a general framework
for quasi two-dimensional magnetohydrodynamic flows. Not only can this model
account for otherwise disconnected past results, but it is also used to predict
a new type of shear layer, of typical thickness Ha^{-1/4}.
