610 
21 m sec. The corresponding vertical velocity is then 
about —2.8 cm sec. This is the order of magnitude of 
the vertical wind components in the vicinity of the 
polar front. 
Air particles (B in Fig. 6) situated at greater dis- 
tances from the principal front probably move almost 
horizontally and thus follow approximately the contour 
lines on the corresponding chart. Since the air at the 
500-mb level usually moves faster than the upper dis- 
turbances, a given particle leaves one trough and moves 
into the next trough. Thus the idea of a quasi-horizontal 
large-scale wave motion is much more applicable to the 
air masses far away from the polar front. 
The three-dimensional movement outlined here has 
some resemblance to the helical circulation proposed by 
Mintz [38]. In our scheme, however, there is no com- 
plete left-handed helix, since the transformation of polar 
air into tropical air, and vice versa, is a much more 
complicated process than that assumed in the simple 
model for helical motion. 
The movement of a tropical air parcel can be studied 
in the same way. In this case it is more practical to start 
from the surface map and discuss the three-dimensional 
trajectory of a tropical air parcel situated at the be- 
ginning in the vicinity of the polar front. A study of the 
large areas of condensation and precipitation around the 
principal front shows that the warm air in that vicinity 
must be subjected to vertical movements of an order of 
magnitude varying between 1 and 20 cm sec. Thus 
the ascending warm air can rise from the surface layers 
to the level around 600-500 mb in one day or less. In 
many cases this rapid ascending motion stops before 
the air reaches this level, but a careful study of 500-mb 
charts indicates that moist, almost saturated air, with 
a potential wet-bulb temperature characteristic of the 
surface tropical air farther to the south, can be observed 
in the region above the polar-front surface. The princi- 
pal area of extended precipitation on the eastern side of 
_ the upper trough and in the region of the upper ridge 
indicates where the principal ascent of the tropical air 
takes place. 
Synoptic experience thus gives some clues concerning 
the nature of the vertical circulation necessary to main- 
tain the kinetic energy of the atmosphere. The vertical 
circulation is mainly associated with cyclones and anti- 
cyclones. The principal regions of descending polar air 
are the cold anticyclones separating cyclone families 
(or individual cyclones) and their counterparts in the 
free atmosphere, the cold troughs. The tropical air 
ascends in the regions where condensation and precipi- 
tation are observed. 
The scheme presented in Figs. 5 and 6 is not a steady- 
state situation. It represents a certain stage in the 
development which gradually leads to a degeneration 
and ultimate elimination of the upper trough. Before 
we go on to a discussion of that process, however, we 
must study the development of the typical frontal 
cyclones. 
According to the generally accepted theory for the 
development of individual cyclones, kinetic energy is 
MECHANICS OF PRESSURE SYSTEMS 
produced by a solenoidal circulation connected with 
sinking of cold air and the ascent of warm air during the 
occlusion process. The occlusion process in lower layers 
is associated with convergence and an increase of cy- 
clonic circulation (vorticity). The ascending warm air 
must form a diverging current in the upper troposphere. 
The convergence at lower levels and the divergence at 
upper levels associated with a general ascending move- 
ment represent one branch of the solenoidal circulation, 
the other branch being the combined lower divergence 
and upper convergence associated with descending 
movement in the surrounding cold anticyclonic areas. 
It is a well-known fact that durmg the occlusion 
process the cyclonic circulation gradually spreads to 
deeper layers of the atmosphere. In a fully developed 
occluded cyclone, which in the lower troposphere is cold 
compared with the surrounding air, a strong cyclonic 
circulation occupies the whole troposphere and the 
lower stratosphere. However, increasing cyclonic circu- 
lation presupposes convergence, according to V. Bjerk- 
nes’ circulation theorem, and the ascending warm air 
in an occluding system must be subjected to upper 
divergence. 
This dilemma has been discussed by Brunt [12] in an 
article on cyclones. In his article, Brunt points out that 
the upper-level divergence necessary to produce the 
pressure fall in the central parts of a deepening cyclone 
must result in increasing anticyclonic circulation in the 
upper troposphere. The dilemma can be solved, accord- 
ing to Brunt, only if the three-dimensional structure of 
the cyclone is such that the upper current can remove 
the air accumulating in the region of lower convergence. 
This removal is not possible if the extratropical cy- 
clones are symmetrical and, at the same time, the 
cyclonic circulation is increasing in depth. Here we find 
one of the principal differences between extratropical 
and tropical cyclones.® In order to find a model which 
combines the increase in cyclonic circulation with the 
divergence necessary for removal of the air from the 
deepening cyclone, we apply J. Bjerknes’ tendency 
equation [6] to a vertical air column situated over the 
momentary surface center of the cyclone. The pressure 
change at a level h is then given by 
ea Sie if div (pv) dz + (gow)n. (12) 
At the surface, where the vertical component w is zero, 
the pressure tendency is given by the integrated mass 
divergence over the whole air column. Since the pres- 
sure in a deepening cyclone is falling, the integral of the 
mass divergence must be positive; since there is low- 
level convergence during the occlusion process, the 
upper-level mass divergence must be somewhat stronger 
than the low-level convergence. 
9. The central parts of tropical cyclones are warm compared 
with the outer parts [51]. The cyclonic circulation therefore 
decreases upward in tropical cyclones whereas it increases up- 
ward in fully developed occluded extratropical cyclones. 
