Geology Reference
In-Depth Information
1.10
axial
1.00
CORE11
PREM
0.90
1066A
Cal8
Observed
3.0
4.0
5.0
6.0
7.0
Unsplit period
T
0
in hours
Figure 8.17 Splitting curves for the three translational modes. The inviscid curves
for the three modes are shown as dashed, based on the splitting parameters for
Earth model Cal8 (open squares). Inviscid periods are overplotted for Earth mod-
els Core11 (open stars), PREM (open diamonds) and 1066A (open triangles).
Solid viscous splitting curves are for a single viscosity. The observed periods
(solid circles) fall on the viscous splitting curves to better than 5 parts in 10
4
for
a single viscosity of 1.225
10
11
Pa s. The dashed curves surrounding the viscous
×
curves are those for a
±
20% variation of viscosity.
where
T
is the period,
T
0
is the unsplit period,
T
s
is the length of the sidereal
day and g
ν
is a dimensionless viscous splitting parameter. For the axial mode, the
viscous splitting parameter is related to the inviscid splitting parameter g
i
by
i
1
E
k
f
a
(σ)
M
I
M
I
−
1
4
g
ν
=
g
+
,
(8.114)
M
I
+
α
and for the equatorial modes by
i
1
M
I
−
β
M
I
E
k
f
e
(σ)
M
I
+
α
M
I
1
8
g
ν
=
g
−
+
β
+
,
(8.115)
+
α
where
E
k
is the Ekman number while α and β are coe
cients of the pressure drag
on the inner core given by
⎝
⎠
,
(
a
/
b
)
3
M
S
1
2
+
3
2
M
I
+
α
=
M
I
M
S
1
(
a
/
b
)
3
(8.116)
+
−
M
O
Search WWH ::
Custom Search