EXTRATROPICAL CYCLONES 
The denominator in the expression above can be de- 
termined uniquely from the data contained in the pro- 
file, whereas the numerator depends on derivatives of the 
geostrophic wind normal to the profile and derivatives 
in time. Let us consider the denominator first. 
Along the lower part of the 293° isentrope the geo- 
strophic shear 0v,/dn is negative, and hence 20, — 
dv,/0n is large. Between the points of intersection of 
the 293° isentrope with the isovels of 20 m sec and 
10 m sec the value of 22, — 0v,/dn can be computed 
to be 1.6 X 10~* sec, as indicated at the bottom of the 
profile. Farther up along the 293° isentrope, dv,/dn 
changes sign and 20, — dv,/dn decreases despite the 
northward increase of 2©,. In the baroclinic field be- 
tween Rapid City and Glasgow 20, — dv,/dn has de- 
creased to 0.8 X 107‘ sec. Still smaller values are 
found along the 282° saturation isentrope, and a nega- 
tive 20, — 0v,/dn results in the section near Rapid 
City. The latter value indicates dynamic instability or, 
in other words, the condition of upgliding without dy- 
namic brake action. Actually only small volumes of 
saturated air (altostratus and cirrus) occur in the region 
under consideration during the early stage of fronto- 
genesis, and friction of such air agamst the dry en- 
vironment probably exerts enough of a brake action 
to preclude violent developments. The dry-adiabatic 
upgliding thus still applies to the greater part of the 
baroclinic upper-tropospheric air. 
The numerator in the expression for v, can be judged 
from an inspection of the 500-mb map (in Fig. 11). 
If v,0v,/d% is measured on the map just north of Rapid 
City, it amounts to 20 X 2.6 X 10 m sec = 5.2 X 
10~* m sec. The large value of the term comes from 
the convergence of the 500-mb contours and that 
feature, in turn, is inherent in the structure of the large 
pressure trough to the west with its central area of weak 
pressure gradient bordering on strong pressure gradients 
to the south. The large value of 0v,/dx is, of course, 
also corroborated by measured wind velocities, which 
increase from 10 m sec™! to 50 m sec“ along the stream- 
line from northern Wyoming to Green Bay, Wisconsin. 
In addition, the 300-mb map (Fig. 9) shows the same 
convergence of contours a little farther north. 
An evaluation of v, at the 500-mb level just north 
of Rapid City gives 
y, = 22 X 107 
1 O8 5e1o= 
Here dv,/dt has been neglected as insignificant in com- 
parison with v,dv,/dx. The corresponding v, would be 
about one-hundredth of v, , hence 6.5 em sec”!. Cor- 
responding determinations of v, lower down on the 
frontal slope result in smaller values, and consequently 
0v,/0n is positive. With dv,/dn and dv,/dx both positive 
in the frontal zone, there is stretching in both the 
y-direction and the x-direction, so that frontogenesis 
progresses under optimum conditions. 
In the upper troposphere south of the maximum 
westerlies dv,/dy assumes large values approaching those 
of 20, . In Fig. 11, 20, — 0v,/dn measured at 300 mb 
over Oklahoma City is only 0.1  10~* sect. However, 
= 6.5msec . 
093 
Vz00,/0% + dv,/dt is also small at that place (see Fig. 9) 
so that no great v,-component results. Farther east 
near the Atlantic, where the anticyclonic isentropic 
shear is equally great and v,0v,/dx has a large negative 
value, v, is observed to have a large negative value 
(directed towards high pressure) at all reporting upper- 
wind stations. This is an example of the systematic 
nongeostrophic wind components at the ‘‘delta”’ of an 
upper jet stream derived in Fig. 8. The horizontal con- 
vergence resulting in the southern half of the delta is 
instrumental in providing the pressure rise ahead of the 
moving high in the southeastern United States (Fig. 
10). 
Figure 12 shows a profile through the zone of fronto- 
genesis twenty-four hours later. The frontal slope has 
become steeper (469 in the lowest portion) and the 
frontal shear —dv,/dy is now characterized by a sharp 
180° wind shift. Negative v, values (northeast wind) 
stronger than 10 m sec~! now occur in the lower part 
of the cold wedge near the front. Applying the 2,- 
formula to particles in the northeast current, we find 
conditions set for isentropic downgliding because the 
numerator v,dv,/0% + dv,/dt is now negative. A nu- 
merical estimate of the downgliding along the 281° 
isentrope near the cold edge of the frontal zone at 850 
mb follows: 
OVg , Og 
; * Ox zt at 
= 
XO, Vo 
on 
—10 X 14 x 10° — 10 * ee 
Mat ose 
The resulting dry-isentropic descent traverses the 
frontal zone with a component from the cold to the 
warm side. This nongeostrophic component towards 
the frontal trough, together with the frictional flow 
component in the same direction, accounts for the sub- 
geostrophic displacement of warm fronts in general. 
In some cases the nongeostrophic component normal to 
the front may permit the cold wedge to advance against 
a moderate geostrophic component from warm to cold. 
In the upper part of the frontal zone, isentropic up- 
gliding continues on November 8 just as on November 
7, as can be seen from the convergence of contours be- 
tween Omaha and Bismarck on the 500-mb map (Fig. 
12). The same contour convergence is found right over 
Omaha on the 700-mb map (not reproduced). In the 
profile the 284° saturation isentrope approximately fol- 
lows the warm edge of the frontal zone; dv,/dn measured 
along that isentrope gives values greater than 20 
from the condensation level up to 700 mb. This lower 
portion of the frontal zone is thus dynamically unstable; 
while higher up, where the 284° isentrope turns parallel 
to the v,-isovels, finite speeds of upgliding can be de- 
termined. An estimate of the upgliding on the saturation 
isentrope of 284° at the 500-mb level gives 
1 PE SOUS WO 
T AO = Oil) Se io= 
= 3.6msec . 
Vy 
