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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 (40View Equation) 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
L =_ rsinh (_O_r sin h + <vf>), (68)
FMC =_ r-<v >L, (69) M
(< > < > ) FRS =_ rrsinh v'rv'f ^r + v'hv'f h^ , (70)
( ) FMS =_ - rsinh- <B'B' >r^+ <B' B' >h^ , (71) 4p r f h f
MT rsinh F =_ - -4p---<Bf ><BM > , (72)
{ ( ) ( ) } 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.
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