Geoscience Reference
In-Depth Information
thumb will point in the direction of v .) Absolute angular momentum per unit
mass, M , is
(6.7)
Mvr
.
Observations of atmospheric and ocean circulation are invariably presented
in the rotating, noninertial frame of reference. The winds and currents in chap-
ters 2 and 3, for example, represent velocity relative to the rotating earth, but
the motion of a parcel is constrained by conservation of angular momentum in
the absolute (inertial) frame of reference. For observers in the rotating frame of
reference (like us), a parcel will seem to have forces acting on it when, in fact,
there are no true forces acting on it; the parcel is simply conserving absolute
angular momentum.
Consider a unit mass parcel of air or ocean water, diagrammed in Figure
6.2. (The size of the parcel as well as its distance above the earth's surface,
z , are drawn wildly out of scale.) If the parcel has no velocity relative to the
rotating earth, then
  where the local Cartesian coordinate system
(Appendix B) rotating with the earth is used. In this case, the parcel is said to
be in solid body rotation with the earth. Viewed from the absolute frame of
reference, in which angular momentum must be conserved, the parcel is not at
rest but traveling in a circle of radius r , completing one circuit every 24 hours.
The tangential velocity of the parcel in the inertial frame of reference is
uvw
0,
2
π
(
az
+
) cos
φ
,
v
=
(6.8)
T
24 hr
Ω
k
r = ( a + z ) cos
ϕ
z
a
ϕ
Figure 6.2. An air or ocean parcel in solid body
rotation.
 
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