604 
clone theory. As long as fronts were regarded as sur- 
faces of discontinuity of the order zero (Margules’ type) 
every front was characterized by cyclonic shear. Since 
real fronts always have a certain width, the principle 
of cyclonic shear can no longer be sustained in its 
original form. Analyses of charts for different levels 
show that although most fronts are characterized by 
cyclonic shear, fronts with anticyclonic wind shear are 
not uncommon at the level around 700 mb, whereas 
practically all fronts in the vicinity of the earth’s sur- 
face and in the middle and upper troposphere (above 
600-500 mb) are characterized by cyclonic shear. 
Another characteristic of the westerlies is that there 
seems to be an upper lamit for the anticyclonic shear of 
the west wind. This limit is determined by the rule 
that the absolute angular momentum about the earth’s 
axis should not increase northward along a horizontal 
surface. This rule of “dynamic stability,” first formu- 
lated by Helmholtz [26], has been further developed 
and used by Solberg [58], Hgiland [28], Kleinschmidt 
(81), Van Mieghem [61, 62], and others, and has been 
combined with the hydrostatic stability. 
The upper limit for the meridional shear in the case 
of a dynamically stable zonal motion is given by 
a = 90) gin oy te © tem eh. (8) 
oy a 
The second term on the right depends upon the hori- 
zontal component of the radius of curvature for zonal 
flow. Since the absolute vorticity ¢. about a vertical 
axis is expressed by 
fa = 29 sin 6 + © tan $, (9) 
equation (8) also expresses the rule that the absolute 
vorticity is negative for a dynamically unstable zonal 
motion. 
In the use of upper-air charts the real wind is com- 
monly identified as the geostrophic wind. In many cases 
the geostrophic wind gives a sufficiently good approxi- 
mation to the real wind. However, one must be careful 
in using the geostrophic approximation im determining 
the upper limit for the anticyclonic wind shear. If 
equation (8) is expressed by the geostrophic wind 4, , 
the following equation for the upper limit of the shear 
of the geostrophic wind [41] should be used: 
Oy og in 6 OB ton as 
oy a 
(10) 
The difference is considerable. If, for example, at lati- 
tude 45°N the geostrophic wind at the tropopause level 
is 80 m sec (not an unusually large value), the critical 
shear for the geostrophic wind is 1.41 X 107* sect. 
The corresponding gradient wind (radius of curvature 
of the trajectory equals a/tan ¢) is only 73 m sec and 
the critical shear for the gradient wind is 1.14 X 
10 sec. 
The foregoing results are valid only if the isentropic 
surfaces are horizontal. In other cases the shear should 
MECHANICS OF PRESSURE SYSTEMS 
be determined along a corresponding isentropic surface 
or, in cases of condensation, along a surface of constant 
wet-bulb potential temperature. In cases where the 
slope of these surfaces is not too great the formulas for 
the critical shear given above can be used; in cases where 
the slope is greater there should be a corresponding 
correction. If the shear exceeds the critical value, the 
air flow is dynamically unstable because in such a case 
the stabilizmg mfluence of the inertial force vanishes. 
The importance of this type of instability will not be 
discussed further here since the problem is treated by 
J. Bjerknes m his contribution to the Compendium. 
It might, however, be pointed out that the critical 
shear represents an interesting analogy to the adiabatic 
lapse rate of temperature as the upper limit for the 
vertical temperature gradient in the atmosphere. 
The foregoing rule concerning the upper limit for the 
anticyclonic shear south of the zone of maximum wind 
should be modified if applied to disturbances, since the 
curvature of the air flow then becomes of major im- 
portance. 
Since the existence of a well-marked jet stream in the 
upper troposphere is associated with the existence of a 
strong concentration of the meridional solenoid field, 
a real jet appears on hemispheric upper-tropospheric 
charts only m regions where the polar front im the 
middle troposphere is relatively well marked. This 
means that the jet in actual cases should not be con- 
sidered as a hemispheric phenomenon without inter- 
ruptions. A distinct jet stream, as well as a distinct 
polar front, must be the result of a certain type of dis- 
turbance acting frontogenetically. If we use the con- 
cept of a hemispheric polar front or hemispheric jet, we 
do not intend to emphasize that both phenomena should 
necessarily be fully established around the whole hemi- 
sphere. 
In mean upper charts and meridional cross sections a 
relatively well-marked jet stream appears, especially 
in winter, at latitudes around 20°-40°N according to 
Namias and Clapp [39]. Also, in mean meridional cross 
sections studied by Willett [63], Hess [27], and Chaud- 
hury [15], and for the Southern Hemisphere by Loewe 
and Radok [82], a similarly low latitude for the maxi- 
mum westerlies was found. Since the average position 
of the polar front at the 500-mb level appears to be 
around latitude 45°-50°N, one should expect to find the 
maximum west wind near this higher latitude. The belt 
of maximum west wind associated with the upper polar 
front, however, undergoes such strong meridional dis- 
placements and other changes that it could barely be 
recognized in mean cross sections. Therefore the south- 
ern jet on mean cross sections or charts is in Some meas- 
ure another phenomenon probably associated with the 
northern boundary of the subtropical cell of meridional 
circulation. Only in cases of very strong southward dis- 
placement of the polar-front jet stream are both phe- 
nomena combined in one very pronounced belt of maxi- 
mum west wind. This combination of two upper west- 
wind maxima appears to be rather common at some 
longitudes, especially in the vicinity of the meridians 
80°W and 120°R. 
