Geography Reference
In-Depth Information
Fig. 3.1
Rate of change of the unit tangent vector
t
following the motion.
Therefore, the acceleration following the motion is the sum of the rate of change
of speed of the air parcel and its centripetal acceleration due to the curvature of
the trajectory. Because the Coriolis force always acts normal to the direction of
motion, its natural coordinate form is simply
−
f
k
×
V
=−
fV
n
whereas the pressure gradient force can be expressed as
t
∂
n
∂
∂n
−
∇
p
=−
∂s
+
The horizontal momentum equation may thus be expanded into the following
component equations in the natural coordinate system:
DV
Dt
=−
∂
∂s
(3.9)
V
2
R
+
∂
∂n
fV
=−
(3.10)
Equations (3.9) and (3.10) express the force balances parallel to and normal to
the direction of flow, respectively. For motion parallel to the geopotential height
contours, ∂/∂s
0 and the speed is constant following the motion. If, in addi-
tion, the geopotential gradient normal to the direction of motion is constant along
a trajectory, (3.10) implies that the radius of curvature of the trajectory is also
constant. In that case the flow can be classified into several simple categories
depending on the relative contributions of the three terms in (3.10) to the net force
balance.
=
