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:
) and then taking the zonal average of the zonal component. The result may be
expressed as:
where 
![[ ] r^ <BrBh >- <B2 > coth GMT =_ - --- \~/ . <BhB > + ------------f------- 4p r [ 2 < 2>] + -^h- \ ~/ . <B B >- <B-h> +-B-f-- (79) 4p r r](article929x.gif)
![( ) SVD =_ (H -1 - H -1)-@-<v >- 5-H -1 + H -1 1-@--<v > r r n @r h 3 r n r @h r [ ( ) - 1 -1] + H -1 H -1 + 3- + dH-r--+ H-n-- <vh> (81) r r r dr r](article932x.gif)
![2 ( ) @ [ ( 6) dH -1 ]<v > SVhD =_ -- H -r1+ 3H -n1 ---<vr> + H -r 1 2H -n1- H -r1- -- - ---r-- --r-, (82) 3 @r r dr 3](article933x.gif){kind=small}
