A.4 Angular momentum balance

An equation for the conservation of angular momentum in the anelastic system can be obtained by averaging the zonal component of Equation (40

) over longitude and multiplying by the moment arm, $r sin h$ . The result is:

$( ) -@-(rL) = - \~/ . F MC + F RS + F VD + F MS + F MT , (67) @t$

where

${ ( ) ( ) } VD -- 2 -@- <vf> sin-h-@- <vf>- ^ -- 2 F =_ - rnr sin h @r r ^r + r2 @h sinh h = -rnc \~/ _O_. (73)$

As in the remainder of the paper, angular brackets $<>$ denote longitudinal averages and the subscript $M$ denotes the meridional components, e.g., $BM = Br ^r + Bh ^h$ . Note that the net contribution from the magnetic terms $F MS$ and $F MT$ depends only on the magnetic tension, since the longitudinal magnetic pressure gradients (both fluctuating and mean) vanish when integrated over $f$ .