EXTRATROPICAL CYCLONES 
placement polewards. This latter development, which 
does not start until the cyclone is past the nascent 
stage, gains in magnitude with the growth of the 
cyclone. 
In the westerly wave of the upper troposphere, as 
represented in Fig. 1, the air enters the cyclone from 
the northwest and leaves it toward the east, across the 
wave crest ahead of the surface cyclone. As long as 
the upper wave does not degenerate, the relative vortic- 
ity changes sign at the longitude of the inflection points, 
thus changmg from anticyclonic to cyclonic relative 
vorticity m the middle of the upper zone of convergence, 
and from cyclonic to anticyclonic in the middle of the 
upper zone of divergence. This vorticity change by 
divergence is supported by the effect of meridional 
advection. 
The factor (¢ + 20 sin ¢) in the divergence term of 
(6) is equal to the absolute vorticity ¢. of the air rela- 
tive to a nonrotating coordinate system. When ¢ is 
positive (cyclonic), ¢, is large and the individual vortic- 
ity change with time becomes quite sensitive to hori- 
zontal convergence or divergence. If the air is subject 
to a sustamed process of horizontal convergence, its 
eyclonie vorticity will increase without any theoretical 
upper limit. The cyclonic bends of an upper sinusoidal 
westerly are therefore frequently seen to become 
strongly curved. On the other hand, when ¢ acquires 
large negative (anticyclonic) values, the absolute vortic- 
ity may go to zero or even become negative. This 
happens almost exclusively in the upper troposphere 
and lower stratosphere where the wind velocities are 
very strong. On wave crests where ¢, reaches values 
close to zero, the vorticity change is only feebly in- 
fluenced by horizontal divergence, and obeys mainly 
the term of meridional advection in (6). This would be 
equivalent to motion under approximately constant 
absolute vorticity (2 Y 0 orf Y —20 sin ¢. If a wave 
crest in the upper atmosphere has developed to that 
extreme stage, the particles overtaking the crest would 
maintain their anticyclonic vorticity (in the form of 
curvature and/or shear) for a long period thereafter. 
Figure 5 illustrates that case schematically. From an 
initial flow pattern of sinusoidal westerlies (streamline 
1) a “meandering”’ westerly current develops through 
the growth of the wave crest and the deepening of the 
next downwind wave trough (streamlines 2 and 3). 
This development towards meandering flow is not de- 
pendent on the absolute vorticity’s actually having 
reached zero. With absolute vorticities still positive, 
but numerically small, the vorticity change begins to 
react sluggishly to horizontal convergence with the re- 
sult that the sinusoidal perturbation of the westerlies 
begins to degenerate. The meandering development 
may also start from an initially straight current with 
anticyclonic shear close to the value —2Q sin ¢. Any 
small wave impulse may then develop into meandering 
wave patterns. 
It is obvious that the meandering phenomenon, once 
started in regions of excessive anticyclonic vorticity 
in the upper atmosphere, will also have a profound in- 
fluence on the total cyclone picture down to the ground. 
583 
The deepening of the upper wave trough is associated 
with the deepening of the cyclonic vortex underneath, 
and usually also entails a southward component added 
to the normal eastward displacement of the cyclone. 
In all cases of such deepening the initial upper dis- 
turbance must start through the build-up of excessive 
anticyclonic curvature on the wave crest to the west 
of the cyclone. Above the level of nondivergence, the 
divergence term and the meridional advection term in 
(6) are of the same phase, so that the additional terms 
in 0v,/dy and dv,/dx are not likely to affect the general 
pattern of d¢/dt very much. The two levels where their 
influence may be expected to count are (1) close to the 
level of nondivergence, and (2) at the localities where 
3 
Fic. 5.—Successive (1— 3) degeneration of sinusoidal wave- 
pattern caused by excessive anticyclonic vorticity on wave 
crest. 
¢ — 20 sin ¢ 1s near zero. In both cases the competition 
with the divergence term is almost eliminated. Further- 
more, v, and its horizontal derivatives reach their maxi- 
mum in the upper troposphere (about two kilometers 
above the level of nondivergence where | pv. |. has its 
maximum). 
The most compelling reason for admitting a per- 
ceptible influence of the terms in dv,/dy and dv,/dx on 
the variations of ¢ lies in the fact that neither the di- 
vergence term, nor the meridional advection term, nor 
their sum, can account through equation (6) for the 
occurrence of negative absolute vorticity. Analyses of 
observational data do show areas of negative absolute 
vorticity on pronounced upper wave crests and/or south 
of pronounced ‘‘jet streams’ (see Fig. 7). A vertical 
motion effect of the right sign to explain the growth of 
—¢ beyond 20 sin ¢ would be found north of the maxi- 
mum of upward velocity in the cyclone (dv,/dy < 0, 
dv,/dz > 0). The result in terms of a large anticyclonic 
vorticity, and occasionally a negative absolute vorticity, 
can then be expected to accrue on the upper wave crest 
to the east of the cyclone. 
The above reasoning about the vertical motion terms 
in equation (6) has been developed by L. Sherman and 
will appear under his authorship. 
Inertial Motion in Isentropic Surfaces. In slow- 
moving long waves of the upper westerlies, the stream- 
lines relative to the waves almost coincide with the 
streamlines relative to the earth, and the isotherms will 
be moved advectively so as to coincide more or less 
with the isobars. Around the inflection points of such 
long waves we find the best approximation to the 
relatively simple conditions of straight baroclinic flow. 
Frontogenesis and frontal cyclogenesis are frequent 
