Geoscience Reference
In-Depth Information
Ω
ˆ
F
z
k
CENT
ˆ
F
y
j
CENT
φ
n
F
'
n
CENT
ˆ
φ
Figure 6.4. Decomposition of the centrifugal acceleration into
local Cartesian coordinates.
2
u
tan
φ
2
u
t
v
t
F
l
=−
f
2
Ω
u
sin
φ
−
p
j
+
2
Ω
u
cos
φ
+
k
.
(6.23)
d
n
CENT
a
a
This acceleration, representing the centrifugal force per unit mass associated
with nonzero zonal velocity, is part of the Coriolis force.
A parcel with meridional velocity
v
relative to the earth's surface will also
experience centrifugal acceleration. This acceleration, denoted
F
CENT
m
v
, will be
oriented in the local vertical, the
t
direction. Because there is no component of
the earth's rotation in the meridional direction, this centrifugal acceleration is
simply
v
k
2
t
v
F
CENT
m
.
(6.24)
a
THE FULL CORIOLIS FORCE
The full Coriolis force,
F
CO
v
, is constructed by adding the component that ac-
counts for conservation of absolute angular momentum (Eq. 6.16) to the com-
ponents that account for centrifugal accelerations due to zonal and meridional
motion, Eqs. 6.23 and 6.24, respectively:
u
2
tan
φ
uv
uw
i
v
t
t
F
=
2
Ω
v
sin
φ
+
tan
φ
−
2
Ω
w
cos
φ
− +−
f
2
Ω
u
sin
φ
−
p
j
c
m
COR
a
a
a
2
2
uv
k
+
t
(6.25)
+
2
Ω
u
cos
φ
+
.
d
n
a
