582 
often stronger than the temperature change by ad- 
vection. 
Vorticity Analysis of the Extratropical Cyclone. An 
analysis of the vorticity distribution and the history 
of vorticity change of individual parcels in the vortex 
and wave will reveal more of the dynamics of the cy- 
clone. The vertical component of the vorticity ¢ may 
be identified on the horizontal streamline maps as a 
particle rotation about a vertical axis, partly due to 
curvature, v/r. , where 7; is the radius of curvature of 
the streamline, and partly due to shear, —dv/dn: 
SSS ==. (5) 
The rules for determining the algebraic sign can 
always be decided upon by referring to the Cartesian 
component form of vorticity, added as an alternate 
expression in (5). The convention used here is to let 
the positive direction of the coordinate n point to the 
left of the wind, to consider v and r, always positive, 
and to use the positive sign in front of v/7; for cyclonic 
and the negative sign for anticyclonic curvature of the 
streamlines. 
The vorticity change of the individual traveling par- 
ticle [11, 13, 16, 26, 27] is given by the equation, 
dé odpda dpda : ° 
di dxdy dy ox (ar ZU sin) any 
_ 0 cos $) vy + ove (20 cos ¢ + =) (6) 
a oy Oz 
__ 0 av, 
Ox dz 
The first two terms on the right represent in component 
form the effect of isobaric-isosteric solenoids on the 
change of vertical vorticity. These terms are always 
found to be insignificant compared to the following 
ones. The divergence term shows how horizontal ex- 
pansion (divergence) creates negative (anticyclonic) 
vorticity, and horizontal contraction creates positive 
(cyclonic) vorticity. The next term shows the effect 
on relative vorticity ¢ of the displacement of the air, 
either towards the polar regions where the vertical 
component of the earth’s vorticity 2Q sin ¢ is great, or 
towards the equator where 2Q sin ¢ is zero. In the 
absence of the other factors, poleward movement would 
entail a decrease of relative cyclonic vorticity or an 
increase of relative anticyclonic vorticity, and move- 
ment away from the pole would entail an increase of 
relative cyclonic vorticity or a decrease of relative 
anticyclonic vorticity. The last two terms on the right- 
hand side describe the influence of the vertical motion 
in changing the vorticity about the vertical. The term 
involving dv,/dy represents, in part, the fact that the 
infinitesimal disk of air, whose rotation decides the 
value of ¢, arrives at a horizontal position from earlier 
positions with meridional tilt. In terms of relative- 
vorticity change, this is equivalent to a change in 
latitude in addition to that by horizontal meridional 
advection, as can be seen from the analogy between 
MECHANICS OF PRESSURE SYSTEMS 
the terms (20 cos ¢)dv./dy and —(2Q cos ¢)v,/a. Fur- 
thermore, the term in dvz/dy represents the effect of 
rotating the air in the yz-plane so that the vorticity 
about the y-axis, dv,/dz, acquires a vertical component 
at the rate (dv,/dy)(dv2/dz) per unit time. Analogously, 
the last term in (6) represents the rate of change of 
vorticity about the z-axis resulting from a rotation of 
the air in the wz-plane. Usually the terms in dv,/dy 
and dv,/dx are considered to be insignificant in relation 
to the divergence term and the meridional advection 
term, but possible exceptions will be mentioned below. 
In the frontal wave of the lower troposphere, the 
cold air enters the moving cyclone along the warm front 
(Fig. 4). Near the front it has initial cyclonic shear 
Fic. 4.—Motion of warm and cold air relative to the moving 
frontal wave. 
which had been acquired during the period of fronto- 
genesis (see p. 590). The increase of the cyclonic vortic- 
ity in the cold air on its way toward the wave apex is 
due to the horizontal convergence, which extends all 
over the front half of the cyclone (see Fig. 1). This 
creation of relative cyclonic vorticity is somewhat re- 
duced by the effect of the poleward component of air 
travel. Behind the wave apex the air returns southward 
and as a result its relative cyclonic vorticity should in- 
crease. At the same time, however, the air enters the 
region of horizontal divergence, which has the opposite 
effect upon vorticity change. The result is that the air 
which had acquired maximum cyclonic shear along the 
warm front maintains cyclonic vorticity after passing 
the wave apex, but with a simultaneous shift from 
shear to curvature vorticity. The cold air passing at 
greater distance from the center changes from moderate 
cyclonic to anticyclonic vorticity. During the growth 
of the cyclone more and more of the cold air is able to 
maintain its cyclonic vorticity after passing the wave 
apex. 
The warm air in the frontal wave enters the cyclone 
from the southwest. Its speed in lower levels just barely 
exceeds that of the cyclone in its eastward motion. 
Upon arrival at the warm front the warm air climbs the 
receding cold wedge. Again, one branch of anticyclonic 
and another of cyclonic vorticity may be discerned. 
Farthest away from the center, where the horizontal 
convergence is moderate or nonexistent, the warm air 
gains anticyclonic relative vorticity through the pole- 
ward component of movement. Closer to the center, 
where the horizontal convergence is stronger, the warm 
air acquires cyclonic relative vorticity despite its dis- 
