602 
cannot show up very clearly in mean cross sections and 
charts. 
Numerous vertical cross sections normal to the aver- 
age air flow in the free atmosphere have provided de- 
tailed information concerning the structure of tem- 
perature and wind fields in different synoptic situations. 
Figure 1 presents a situation with almost zonal flow 
over North America. The geostrophic wind computed 
from the height of the standard isobaric surfaces shows 
the strong concentration in a wind maximum over 80 m 
sec! between the 300- and 200-mb levels. The maxi- 
mum wind (center of the “jet stream”) seems to be 
associated with a typical break in the tropopause as can 
be seen in Fig. 1. In this special case there seem to be 
three different tropopauses: a tropical one around 100 
mb, a subtropical one between 200 and 250 mb, and a 
polar one (with multiple structure) over the northern 
part of the section. 
In Fig. 2 one other situation is represented. In this 
case the vertical cross section is computed along a line 
from southwest to northeast in Europe. The principal 
air flow here is from the northwest and the polar front 
extends from northwest to southeast. In this special case 
the geostrophic northwest wind shows an even stronger 
concentration into a jet than in Fig. 1. Isotherms, isen- 
tropes, frontal boundaries, and tropopause discontin- 
uities show almost the same characteristics as in the 
previous figure. 
If the polar front zone at the 500-mb surface is used 
as a reference for coordinates upon which the mean 
data are computed, it is possible to maintain some of 
the essential features of the meridional temperature and 
wind field found in individual situations. Such a com- 
putation has been made by Palmén and Newton [43] 
for the meridian 80°W. The average temperature and 
wind were correlated with the polar front at the 500-mb 
surface. The cross section can be regarded as repre- 
sentative of cases with predominant zonal air flow.® 
However, if the cross section is to be used on a hemi- 
spherical basis, it must be noted that the average con- 
centration of both meridional temperature gradient 
and west wind is generally more pronounced in the 
meridian used for this cross section than along most 
other meridians. 
Characteristic of the temperature distribution mm the 
vicinity of the polar front is the sloping layer of maxi- 
mum horizontal temperature gradient and pronounced 
vertical stability, and also the rather strong slope of the 
isotherms (strong baroclinity) both above and below 
the frontal surface. This pronounced concentration of 
the meridional temperature gradient in the polar front 
itself and in the layers above and below the sloping 
frontal surface must be associated with a strong con- 
centration of the zonal wind in the upper troposphere 
and the lower stratosphere as can be seen from Fig. 1. 
The equation for the vertical increase of the west 
wind wu (approximately equal to the gradient wind) can 
5. This average cross section is reproduced in Fig. 7 in ‘‘Ex- 
tratropical Cyclones” by J. Bjerknes in this Compendium (see 
p. 586). 
MECHANICS OF PRESSURE SYSTEMS 
be written 
GUE hoe g 1 for 
eee 
2(asin + Stan 6)” 
Here g is the acceleration of gravity, T the absolute 
temperature at the level z, and (07'/dy), the meridional 
temperature gradient measured in an isobaric surface p 
at the same level. The west wind increases up to the 
level where the meridional temperature gradient 
changes its sign (generally at the tropopause level). If 
Umax denotes the zonal wind at that level, one can write 
i a, dz, (5) 
0 7 (asin ¢ + Ztan 6) 
Umax = Uo — 3 
where up is the surface wind and 2; the height of the 
tropopause. Since in most cases the gradient wind at 
the surface is relatively weak, the wind at the tropo- 
pause must be especially strong over the frontal zone 
and relatively weak outside this zone. Thus any pro- 
nounced front with an imclination not too small must 
be accompanied by a strong upper-level wind concen- 
trated into a relatively narrow band. 
The foregoing equations, which are an expression for 
the assumed balance between gravity, pressure force, 
and the resultant of Coriolis and centrifugal forces, do 
not explain the formation of the strong west-wind belt 
at upper levels, but only establish the fact that the 
phenomena appear to be parallel. In cases of strong 
concentration of the meridional temperature gradient 
in the frontal zone, the wind concentration in the upper 
troposphere and lower stratosphere is also strong. In 
such cases it is justifiable to use the name “jet” or “jet 
stream” for the phenomenon. 
The concentration of the pre-existing meridional temper- 
ature contrasts into a real frontal zone or layer (fronto- 
genesis) and the concentration of the zonal wind in a jet 
stream run parallel. Thus any theory for frontogenesis 
should also be a theory for the formation of an upper 
jet stream. 
The frontal layer in Fig. 2 is separated from the two 
principal air masses by surfaces of discontinuity for 
temperature gradient and wind shear, not for tempera- 
ture and wind as in the classical case treated by Mar- 
gules [34]. If the angle of inclination of the surface 
separating the warm air from the air in the frontal layer 
is denoted by w, the change in horizontal wind shear 
du/dy is given [41] by 
du du’ sg tany es Ne (2) ] 6) 
dy dy 20T snd L\ dy /> ay Jr 
In this equation du//dy and (@7’/dy), represent the 
wind shear and temperature gradient in the warm air, 
respectively, and du/dy and (@7/dy), represent the 
same quantities in the frontal zone. 
The horizontal wind shear in the frontal zone becomes 
positive (anticyclonic) if the expression on the right 
