APPLICATIONS OF ENERGY PRINCIPLES 
ent of frictional effects, when the entire atmosphere is 
considered. 
3. In addition to the action of the sources and 
frictional effects, the horizontal kinetic energy in a 
fixed region not embracing the entire atmosphere may 
change due to advection of kinetic energy across the 
boundary and due to the redistribution of kinetic energy 
through the boundary by work done by pressure forces 
and horizontal velocity components at the boundary. 
From the standpomt of the general circulation it 
would appear that the sources of kinetic energy are to 
be found in the regions of horizontal divergence. The 
net contribution from a given level results from the 
fact that areas of divergence generally occur at a 
different pressure than do the areas of convergence. 
Thus at lower levels it is common for horizontal di- 
vergence to be present in anticyclonic areas while con- 
vergence takes place in cyclonic areas, the net result 
being positive. We do not as yet have sufficient obser- 
vational material concerning the distribution of di- 
vergence at higher levels, but the fact that the pressure 
decreases with elevation would seem to indicate that 
the importance of the higher levels rapidly diminishes. 
Generally speaking, it would thus appear that the 
energy sources for the general circulation are to be 
found principally in the subtropical high-pressure cells, 
the migratory polar anticyclones, and the subsiding 
cap of cold air over the polar regions. From these 
primary centers the kinetic energy is continually trans- 
ferred to the cyclonic areas with convergence which 
act as sinks in addition to the action of friction. 
One might ask why it is that if the diverging anti- 
cyclones act as primary sources of kinetic energy, they 
are not the scenes of major activity. Actually, however, 
the generation process cannot be present in such systems 
without the simultaneous operation of the transfer pro- 
cesses. If divergence exists in an anticyclone, the periph- 
eral outward motion results in a rapid outward flow of 
kinetic energy through work done by pressure forces 
and through advection. 
It was pointed out that a transfer of kinetic energy 
of horizontal motions across the boundary of a region 
which is not mechanically closed may be brought about 
by advection of existing kinetic energy and through 
the work done by pressure forces in virtue of the com- 
ponents of horizontal velocity across the boundary. 
Thus, if one considers a symmetrical polar cap extend- 
ing from the north pole to some middle latitude ¢ and 
embracing the entire vertical extent of the atmosphere, 
the expression for the transfer of kinetic energy across 
the vertical southern boundary at the latitude ¢ is 
| Géevin se ip) Gp RS |» eee if Hllbials, (ae) 
m 
where ds is an element of area, R/m is the gas constant 
for air, and 7’ is the absolute temperature, while the 
other symbols have the same significance as previously. 
The approximate equality of the first two integrals 
is based upon the fact that the advection of kinetic 
energy in the atmosphere is of a smaller order of magni- 
571 
tude than the contribution of the term pv except pos- 
sibly at very high levels. The final form depends also 
upon the feasibility of applying the ideal equation of 
state to the atmosphere. If these simplifications are 
accepted, the following observations may be made. 
The last integral is proportional to the advection 
of internal heat energy northward, and hence is in all 
probability positive. This would indicate that there is 
normally a poleward flow of kinetic energy across middle 
latitudes from the tropics and subtropics which ap- 
parently serve as important source regions for such 
energy. Since this flow must cease as the polar regions 
are approached, it follows that the cyclone belts in 
middle and polar latitudes serve as dissipative mecha- 
nisms for this kinetic energy through friction and 
through the horizontal convergence present in them. 
It is a matter of common synoptic experience that 
an extratropical cyclone is more apt to intensify if 
there is a relatively large contrast in the heat advection 
on its eastern and western sides. According to the 
present discussion, it is not essential that the imcrease 
of kinetic energy in such cases be produced im situ 
through conversion from other forms of energy. The 
intensification may be brought about through the in- 
creased local poleward transport of kinetic energy 
from the general source region in lower latitudes, as 
measured by the large net local heat transport pole- 
ward. 
We have made the tacit assumption in the develop- 
ment given above that the “frictional”? term D leads 
to a dissipation of kinetic energy. If only molecular 
viscosity and small-scale turbulent viscosity are in- 
cluded in this term, the assumption is undoubtedly 
valid. However, if relatively large-scale eddies and 
other large features of the atmospheric motions are 
included in the form of a gross turbulence as distin- 
guished from the remaining mean motion, it is apparent 
that the quantity D may then embrace energy-produc- 
ing systems and it is possible that it may change sign. 
Thus, for example, if only the average zonal circulation 
of the atmosphere be considered as the true mean mo- 
tion so that the cyclones, anticyclones, and other non- 
zonal motions appear as turbulence, there is no clear 
a priori reason for assuming that the term D represents 
a dissipation. 
Finally, it is interesting to compare the results ob- 
tained here with those of Margules [5] in his classic 
paper, ‘‘On the Energy of Storms.” Very broadly speak- 
ing, the two approaches deal with essentially the same 
process. We have simply enlarged the ‘‘chamber”’ con- 
taining the gas used by Margules so as to include the 
whole atmosphere. Furthermore, whereas Margules con- 
sidered a discrete process, we have replaced it by a 
continuous one and restricted our attention to the 
production, redistribution, and dissipation of kinetic 
energy of horizontal motions only. Also, we have recog- 
nized that under these circumstances the pressure multi- 
plied by the horizontal divergence is the measure of the 
rate at which other forms of energy such as potential 
and internal energy are being converted into kinetic 
