Geoscience Reference
In-Depth Information
6
DYNAMICS: THE FORCES
THAT DRIVE ATMOSPHERIC
AND OCEAN CIRCULATIONS
In
chapter 5
we showed that the longwave and shortwave radiative heat fluxes
at the top of the atmosphere do not balance locally—there is net radiative heat-
ing in the tropics and radiative cooling at high latitudes (see
Fig. 5.9)
. Why,
then, are temperatures in the tropics not continually increasing and those at
high latitudes decreasing? The reason is that atmospheric and ocean circulation
systems move heat from the tropics to higher latitudes to balance local radia-
tive heating and cooling.
To understand these circulation systems, the forces that drive and constrain
them can be accounted for by applying Newton's second law,
v
/
v
Fma
,
(6.1)
to a parcel of air or ocean water. (A
parcel
is a unit of air or ocean water,
defined either as a unit mass or a unit volume.) In Eq. 6.1, the summation in-
dicates that various forces act on parcels to determine acceleration. That accel-
eration, of course, generates velocity—wind or ocean currents—which changes
according to
/
v
F
v
dv
.
(6.2)
m
dt
The use of the total, or Lagrangian, derivative in Eq. 6.2 (see Appendix C)
indicates that the perspective is one of following the parcel, much as Newton's
first law of motion is often illustrated in physics textbooks by adding the forces
acting on a block as it slides down an inclined plane. The translation from the
Lagrangian to the Eulerian perspective, which deals with motion relative to a
given location in a coordinate system, is discussed below and in Appendix C.
First, the most important forces that govern large-scale motion in the atmo-
sphere and oceans are assembled for the summation in Eq. 6.2.
The scalar components of the vector equation, Eq. 6.2, are known as the
equations of motion
or the
momentum equations
. Using the local Cartesian
coordinate system defined in Appendix B, we have
/
F
x
du
x
x
x
==++
F
F
F
,
(6.3)
m
COR
PGF
F
dt
/
F
y
dv
y
y
y
==++
F
F
F
,
(6.4)
m
COR
PGF
F
dt
