### A.5 Meridional circulation maintenance

An equation for the maintenance of the circulation can be obtained by applying a curl to the
momentum Equation (40) and then taking the zonal average of the zonal component. The result may be
expressed as:
where is a unit vector directed perpendicular to and away from the rotation axis. The
flux vector is given by
where the components include the Reynolds stress
the advection of vorticity by the meridional circulation and differential rotation
buoyancy
magnetic tension
and viscous diffusion
where the radial and latitudinal components of are given by
and
and where and are the scale heights for the density and viscosity: