Geoscience Reference
In-Depth Information
β
d
=
β/
K
2
+2
F
U
s
k
1
,
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−
v
s
=
U
d
k
1
,
v
d
=
U
d
K
2
2
F
/
K
1
+2
F
k
1
,
γ
s
=16
k
1
/(
16
K
2
)
,
γ
d
=16
k
1
k
1
−
−
2
F
/
6
K
2
+2
F
,
γ
b
=32
Fk
1
/
3
π
2
+2
F
.
(B.3)
The model by
Lovegrove et al.
[2002] consists of four
equations for the baroclinic wave of zonal and radial
mode numbers
m
and
n
= 1, respectively, in terms of
the cosine component
C
and sine componen
S
for the
barotropic and baroclinic vertical modes using subscript
s
for sum or barotropic and
d
for difference or baroclinic, as
well as an equation for a single mean-low correction term,
A
. The coupling between the standard model by
Lovegrove
etal.
[2002] and the boundary layer adds equations for the
temperature at the interface between the interior and the
Stewartson layer
θ
in the forms
C
s
=
−
s
C
s
+
β
s
S
s
−
(v
s
+
γ
s
A) S
d
,
S
s
=
−
β
s
C
s
−
s
S
s
+
(v
s
+
γ
s
A) C
d
,
(B.4)
C
d
=
−
(v
s
+
γ
d
A) S
s
−
d
C
d
+
β
d
S
d
,
(B.5)
S
d
=
(v
s
+
γ
d
A) C
s
−
β
d
C
d
−
d
S
d
,
(B.6)
A
=
γ
b
S
d
C
s
−
γ
b
C
d
S
s
−
b
A
,
(B.7)
b
δ
A
,
θ
=
−
(B.8)
b
δ
Pr)
θ
+
+
1
1
Pr
(
1+
gS)
.
(B.9)
−
Pr
+
v
n
exp
(
−
While the effect of the waves on the interface temperature
is explicit, the reverse effect is implicit in the fact that the
forcing parameter as defined equation (B.1) depends on
the interface temperature.
REFERENCES
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ScatteringTransform
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,
34
, 301-317.
Barcilon, V., and J. Pedlosky (1967), A unified linear theory of
homogeneous and stratified rotating fluids,
J. Fluid Mech.
,
29
,
609-621.
