EXTRATROPICAL CYCLONES 
anticyclonic bend over western Canada on November 7 
and the following days shows that mstances of r; < 
Tmin are quite frequent, in other words, that with the 
given pressure gradient and contour curvature the paths 
of particles often cannot have as small a radius of curva- 
ture as that of the isobaric contours. If that applies to 
a quasi-stationary pressure ridge like the orographic 
one over the Canadian Rockies, where the radius r, 
of streamline curvature is equal to the radius r of path 
curvature, the air would have to cross the isobars 
towards low pressure while making the anticyclonic 
turn. This must imply a forward acceleration of the 
particle leading up to maximum speed at the end of the 
anticyclonic sweep. If such fast-moving air is fed 
directly into a pressure trough downstream, in which 
the pressure gradients were adapted to smaller wind 
speeds, an intensification of the trough should follow. 
The deepening of the large pressure trough over western 
and central United States during November 7-9, 1948, 
should probably be interpreted this way. Measured 
winds are unfortunately not available for a complete 
check of these ideas. The only part of the phenomenon 
that can be well demonstrated is the general occurrence 
of wind components towards high pressure, resulting 
from the supergeostrophic velocity of the air that is 
leaving the anticyclonic bend (see winds over the 
western United States on the 300-mb map of November 
8, 1500Z). 
The flow around the quasi-stationary anticyclonic 
bend over western Canada cannot be a steady-state 
one, although the major features of that part of the 
map do remain unchanged. The 300-mb maps show 
how one moving wave perturbation after the other 
appears on top of the large stationary crest of high 
pressure in the west. The first of these traveled about 
1500 km during twelve hours (85 m sec) and is found 
on the second map with its wave crest in the northerly 
current at the Canadian-United States border. The 
300-mb contour curvature at that time and place de- 
fines an 7; which is much smaller than fmin - 
The radii of curvature of streamlines, r, , and of air 
trajectories, 7, in a moving sinusoidal wave, are related 
to each other by the formula 
te 5 (16) 
) 
constants. Solving (12) for 
y 2 
2 (13) 
ae 29.0 + O@/dr 7 w@ = Vg)” 
and seeking the value of v for which r is a minimum, we obtain 
Ob 
6 
0 = — = %,. (14) 
The corresponding values of 7min and v are thus 
ke 
or 2v, 
alt = a au v = 2v, (15) 
589 
where ¢ is the speed of the wave. No measured wind 
velocities are available at 300 mb in western Canada 
during the days under consideration. Theoretical es- 
timates of v must lie between v, and 2v, , and are most 
likely closer to the lower than the upper limit, as will 
be shown later. Assuming tentatively for the moving 
pressure crest at the Canadian—United States border 
on November 8, 0300Z, v = 1.lu, = 49 m sec™!, we 
would have from (13) 
49° 
"= 1.08 x 10-449 — 445) 
= 4900 km, 
and would arrive at the following estimate of 7; : 
549 — 35 
rs = 49 X 10 49 
m = 1400 km, 
which is much longer than the measured radius of 
contours r; = 440 km. These estimates and measure- 
ments are of course subject to great errors, but even 
so, the conclusion seems to be that also on the moving 
pressure crests the streamlines will fail to adapt to the 
strong curvature of the isobars. It then also follows 
that the moving pressure crests at the 300-mb level 
are preceded by a velocity maximum. When the air 
from that velocity maximum enters the slow-moving 
low-pressure trough, a pulse of deepening by centri- 
fugal action would result. The rapidly moving upper 
wave cannot be seen to continue its propagation on the 
front side of the deep slow-moving trough. Hence all 
its wave energy must have been absorbed in the large 
trough. 
With the above estimate of »v = 49 m sec and r,; = 
1400 km, the anticyclonic vorticity due to curvature 
—vy/r, amounts to —3.5 X 10 sec. This is numer- 
ically much less than 29 sin 50° = 1.1 X 10 sec, so 
it does not seem likely that the complete anticyclonic 
vorticity —v/r; — dv/dn reaches the critical value of 
—2Q, anywhere in the rapid wave at 300 mb. The 
described manifestation of mstability through cross- 
isobaric flow on the anticyclonic bend thus takes place 
independently of the fulfillment of the criterion 
—v/r; — dv/dn + 20. < 0. 
On November 8, 1500Z, when the most unstable part 
of the anticyclonic flow was found far north (again 
marked by 7; < rmin), @ growing crest and a downwind, 
deepening trough formed simultaneously. When that 
perturbation caught up with the slow-moving trough 
ahead, another deepening occurred (see November 9, 
1500Z), this time in the north-central United States 
while the southern end of the trough was losing depth. 
These fast-moving unstable waves on the 300-mb 
maps are, of course, at times connected with disturb- 
ances in the lower atmosphere. The first of the upper 
waves was formed on November 7, 1500Z, as an oc- 
cluded front was approaching from the west; it is likely 
that the excessive anticyclonic curvature resulted from 
a superposition of the upper wave crest (associated 
with the occluded cyclone) upon the semipermanent 
anticyclonic bend produced orographically by the 
northern Rocky Mountains. Once formed, the unstable 
