  Gough & McIntyre have suggested that the dynamics of the solar tachocline are
dominated by the advection-diffusion balance between the differential rotation,
a large-scale primordial field and baroclinicly driven meridional motions. This
paper presents the first part of a study of the tachocline, in which a model of
the rotation profile below the convection zone is constructed along the lines
suggested by Gough & McIntyre and solved numerically. In this first part, a
reduced model of the tachocline is derived in which the effects of
compressibility and energy transport on the system are neglected; the
meridional motions are driven instead by Ekman-Hartmann pumping. It is shown
that there exists only a narrow range of magnetic field strengths for which the
system can achieve a nearly uniform rotation. The results are discussed with
respect to observations and to the limitations of this initial approach. A
following paper combines the effects of realistic baroclinic driving and
stratification with a model that follows closely the lines of work of Gough &
McIntyre.
