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of the fluid, while both
n
and
n
g
denote unit vectors orientated towards the center
of the Earth, with
n
being orthogonal to the integration surface and
n
g
normal to the
equipotential at
S
(de Viron et al.
2001a
).
Obviously, the total interaction torque between the Earth and the atmosphere is
composed of three parts, see e.g. de Viron and Dehant (
1999
): a pressure torque
L
p
acting on the topography, a gravitational torque
L
g
corresponding to the attraction
of the atmospheric mass by Earth's nonspherical mass, and a friction torque
L
f
due
to the local friction drag associated with atmospheric surface winds. We will now
address those three components in more detail.
Pressure Torque
Speaking in terms of the atmospheric torque acting on the solid Earth (left-hand side
of Eq.
56
), the pressure torque is generated by the pressure forcing of fluid masses
on the topography. As initially shown by Wahr (
1982
), the equatorial component of
this torque has to be separated into two parts: a global pressure torque acting on the
ellipticity of the Earth and a so-called
mountain torque
on the local topography. This
local pressure torque arises from the differential action of surface pressure on the
two faces of mountain ranges (de Viron et al.
2001b
) as depicted in Fig.
7
. Hence, it
can be estimated by multiplying the gradient of
p
s
=
p
s
(θ, λ)
with the radius arm
a
. Herein, the quantity
a
denotes the radius
of a mean spherical Earth, while
h
is the elevation of the topography bar the effect of
ellipticity. The corresponding analytical expression is given by de Viron and Dehant
(
1999
)
+
h
(θ, λ)
at co-latitude
θ
and longitude
λ
p
0
+dp
s
h
p
0
d
friction
force
θ
=const
zonal winds
Fig. 7
Illustration of pressure torque and friction torque in the axial direction as seen from the north
pole. An exaggerated topographic feature at co-latitude
is subject to a zonal pressure gradient force
of magnitude d
p
s
. Local surface winds give rise to a zonal friction force, which in turn counters
and reduces the depicted westerlies, i.e. the Earth gains angular momentum from the atmosphere
(Salstein
2002
). Figure modified from Wahr and Oort (
1984
)
θ
