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Fig. 8 Torque on the elliptic-
ity of the Earth generated by
the action of a global surface
pressure field that corresponds
to a spherical harmonic term
of degree 2 and order 1
Rotation
axis
L
H
L
Friction Torque
The friction torque on the atmosphere depends on the local tangential wind stress
η
n
·∇
v r , which is a common output of atmosphericmodels in the formof two scalar
fields
representing the friction force on the topography in co-latitudinal and
longitudinal direction, see Fig. 7 . As shown by de Viron et al. ( 1999 ), the full friction
torque vector is composed of
(
f
θ ,
f
λ )
a 3
f θ sin
λ
f λ cos
θ
cos
λ
L f
sin
=−
f θ cos
λ
f λ cos
θ
sin
λ
θ
d
θ
d
λ.
(62)
θ
f λ sin
Feldstein ( 2008 ) gives an identical formulation for the equatorial part of the friction
torque, which is very small except for subdaily frequencies (de Viron et al. 2001b ).
The axial friction torque, constituting 30-50% of the total zonal Earth-atmosphere
torque at different time scales, is treated intensively by Wahr and Oort ( 1984 ).
Having successfully evaluated the different constituents of the total atmospheric
torque in Eq. ( 59 ), one might, in principle, deploy the integral quantity L ( a ) ( s ) =
L ( s ) ( a ) as a forcing function in the Liouville equations. Since the atmosphere
is modeled as external layer to the physical system, the interaction torque has to
be considered in the vector L on the left-hand side of Eq. ( 8 ), see Seitz and Schuh
( 2010 ). Given this condition, it is clear that within the torque approach relative
angular momentum vanishes from the Liouville equations. Likewise, there is also
no contribution of the mass redistribution to the incremental tensor of inertia
I .
Though, similar to what has been outlined in Sect. 2.4 , inertia variations that are
due to rotational perturbations and deformations related to the changing surface load
have to be accounted for. Further details on the inclusion of the interaction torque in
the Liouville equations are given by de Viron et al. ( 2005 ).
Δ
 
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