590 
upper wave separates from the frontal disturbance by 
virtue of its superior speed (85 m sec). The second 
unstable upper wave had no clear connection with any 
frontal disturbance. 
During the selected period, the flow of air east of the 
big slow-moving trough turned gradually from west- 
southwest towards south-southwest while increasing a 
little in strength. On November 8, 1500Z, after the 
cold trough of the Hudson Bay cyclone had moved off 
to the northeast, the upper current over the eastern 
half of the United States and Canada became almost 
straight. On November 9, 0300Z, when the growing 
frontal cyclone (marked by an asterisk on the 300-mb 
maps) began to exert influence high up, the upper cur- 
rent became slightly S-shaped. The newly formed upper 
wave moved along with the cyclone center below at a 
speed of only 9 m sec. The best estimate of the wind 
speed on the anticyclonic bend is probably 80 m sec! 
(see below) and hence r; = r(80 — 9)/80 = 0.9r. 
Even with r = rmmin = 1950 km, 7, would be 0.9 & 1950 
km = 1760 km, which is greater than the measured 
r; = 1350 km. The streamlines will consequently not 
be able to adapt to pressure contours around the anti- 
cyclonic bend. 
The tentative assumption of r = fmin given above is 
really predicated on the further assumption that the 
wind maintains a speed of 2v, around the anticyclonic 
bend. We can in this case show convincingly that the 
wind does not reach such a speed and therefore that the 
air trajectory must have a radius of curvature con- 
siderably longer than ‘min . 
The geostrophic wind in the strongest part of the 
straight southwesterly current on November 8, 1500Z 
amounted to about 70 m sec, and on the chart for 
November 9, 0300Z a measurement of the geostrophic 
wind in the Great Lakes region gives nearly the same 
value. Even at the geostrophic speed of 70 m sec~, 
which gives a speed of 70 — 9 = 61 m sec™ relative 
to the wave, it would take only 414 hours for each air 
parcel to cover the 1000-km distance along which there 
is anticyclonic curvature. Suppose a particle passes 
the inflection point at 70 m sec and from then on ex- 
periences a forward tangential acceleration (dv/dt), = 
204, on the anticyclonic bend. If v, , the wind com- 
ponent directed outward normal to the isobars, reaches 
the high average value of 10 m sec on the anticyclonic 
bend, the speed of the particles would merease at a 
rate of 10 m sec~! per three hours, and at most by 15 
m sec—! during the whole travel from inflection point to 
inflection pomt. This increase in speed would thus go 
only one-fifth of the way from v, to 2 v, . This reasoning 
justifies the earlier assumption of the moderately super- 
geostrophic wind of 70 + 10 = 80 m sec™ on the 
middle of the anticyclonic bend. 
Another effect of the transisobaric wind component 
on the anticyclonic bend is also worth considering. A 
flow component across anticyclonic contours towards 
low pressure is usually synonymous with horizontal 
divergence of mass, and offers in that way a contribution 
to pressure fall (see equation (1)). The basic pattern 
in Fig. 1 of horizontal divergence in westerly waves 
MECHANICS OF PRESSURE SYSTEMS 
would thus, in the levels of strongest westerlies, show 
the divergence extending forward beyond the ridge of 
highest pressure. The implications of this divergence on 
the pressure ridges of the upper atmosphere for the 
storm development in the lower atmosphere will be 
considered on p. 597. 
Frontogenesis. Figure 10 illustrates three stages of 
frontogenesis, 24 hours apart, represented by simul- 
taneous sea-level and 850-mb maps. At the first map 
time the Hudson Bay cyclone is also shown. Its thermal 
structure is that of an old cyclone with the occluded 
front beginning to wrap around the center. The upper 
warm tongue, extending east and north of the Hudson 
Bay center from the warm-air reservoir over the Atlan- 
tic, is shown clearly in the 850-mb isotherms. The 
pressure trough pointing southwards from the Hudson 
Bay cyclone is not of frontal nature, as can be seen 
from the weak temperature gradient at 850 mb in that 
region. The same nonfrontal trough continues up to 
the 300-mb level (Fig. 9), where its orientation ap- 
proaches northwest-southeast, and in those upper layers 
it actually extends out over the Atlantic, producing a 
bend in the warm sector current. Such troughs always 
move more slowly than the air, and it is kinematically 
impossible for fronts to develop m them. 
Historical continuity made it obvious that the cold 
front from the Hudson Bay cyclone had reached Florida 
by November 7, 1500Z, but the 850-mb map shows how 
the cold air, after arriving over the Gulf States, must 
have subsided and thereby effaced most of the frontal 
temperature contrast. The bundle of isotherms running 
along the northern part of the cold front bends west- 
ward over the Carolinas and northern Georgia and 
there marks the intersection of the 850-mb map with 
the tilting surface of subsidence. The 850-mb winds in 
that region blow across the isotherm bundle from cold 
to warm, but fail to produce any local fall m temper- 
ature because of the simultaneous sinking. The de- 
viations from geostrophic flow are quite striking in 
that sinking air mass. While descending from the levels 
of strong west winds the air particles must be retarded 
and, in order to do so, they must move with a com- 
ponent towards high pressure, as shown on the 850-mb 
map of November 7, 1500Z. The same type of geo- 
strophic departure is found on that day over the south- 
eastern United States all the way up to 300 mb (Fig. 9). 
On the following day (November 8), the geostrophic 
departures characteristic of the front side of moving 
anticyclones can be seen on the 850-mb map over New 
England. In the rear of the moving anticyclone the 
opposite geostrophic deviation is observed. In that part 
the air is ascending and accelerating and must have a 
horizontal component towards low pressure. This phe- 
nomenon is actually part of the process of frontogenesis 
over the central United States which will be considered 
next. 
Frontogenesis by horizontal advection operates when 
a field of deformation is maintained in a baroclinic air 
mass. Optimum efficiency in this process is achieved 
when the axis of dilatation of the field of deformation 
coincides with the direction of the isotherms. The 
