586 
but the cause of such an increase of gradient wind is 
not necessarily attributable to the frontal mechanism. 
Whenever v,0v,/0% + 0dv,/dt has the same sign in 
each of the two air masses, v, will also have the same 
sign in the whole field; but its maximum numerical 
MECHANICS OF PRESSURE SYSTEMS 
the line of maximum |v,| . In the stratosphere the 
terms downgliding and upgliding must be interchanged, 
because of the opposite tilt of isentropic surfaces, but 
the statement about the isentropic divergence remains 
identical for stratosphere and troposphere. At the line 
: qt ize : 
SMe 
s SE | 
a ie) Saas 
values, as far as the lower troposphere is concerned, 
will be found in the frontal zone where 20, — dv,/dn is 
at a minimum. 
As shown in Fig. 7, the warm air over the lower and 
intermediate portion of the polar-front surface has 
anticyclonic isentropic shear, increasing to great values 
in the upper troposphere, whereas the air above the 
upper part of the frontal surface has cyclonic shear, 
likewise increasing to high values in the upper tropo- 
sphere. The dividing line between anticyclonic and 
cyclonic shear runs almost vertically through the maxi- 
mum of west-wind velocity, which in the average con- 
dition represented by Fig. 7 is located above the place 
where the frontal surface intersects the 500-mb level. 
Tsentropic upgliding or downgliding as defined by equa- 
tion (11) will reach larger values south of the velocity 
maximum than north of it. It is likely that this differ- 
ence in v, values north and south of the velocity maxi- 
mum does give rise to important horizontal divergence 
effects because the y-component represents a nongeo- 
strophic part of the total wind. The v,-divergence effect 
in the jet-stream region should work out as shown sche- 
matically m Fig. 8. Where there is “confluence” of the 
winds into the western beginning of a ‘jet stream,” equa- 
tion (11) indicates a superimposed isentropic upgliding 
v, > O and “isentropic convergence” dv,/dn < 0 north 
of the line of maximum |v,| . Where the wind velocity 
decreases along the streamlines in the “delta”’ of a jet 
stream, equation (11) indicates isentropic downgliding 
v, < 0 and isentropic divergence 0v,/dn > 0, north of 
0.9 10°Sec 
20, il (Ko) 
Fie. 7.—Meridional profiles through a model of straight westerlies with quasi-stationary polar front (Palmén and Newton 
[24]). Left: Dashed lines show isotherms (degrees centigrade), and solid lines isovels (m sec) of zonal geostrophic wind. Right: 
Dashed lines show the field of dry-isentropes (degrees absolute), and the saturation-isentrope of 281° in the frontal zone. Solid 
lines represent the quantity 2: — dv,/dn in units of 10 sec". 
of maximum |v,| values the isentropic divergence 
dv,/0n changes sign, as shown by the hatching in Fig. 8. 
In figuring out the effect of the isentropic divergence 
in changing the pressure field we may think of the dis- 
tribution of dv,/dn as representing in the first approxi- 
mation a field of dv,/dy, where v, is the nongeostrophic 
\\ 
UY 
ivy z 
cae77 
Fig. 8.—Isentropic convergence (hatched) and divergence 
(unhatched) in the regions of jet-stream confluence and delta. 
CONFLUENCE 
DELTA 
y-component of motion. Assuming that the distribution 
of dpv,/dy can also be qualitatively represented by the 
hatched and unhatched areas in Fig. 8, we have in that 
diagram an outline of the contribution of isentropic 
divergence to the total horizontal divergence. The isen- 
tropic divergence, acting in the same sense through 
