THE WARM FRONT 25 
Pa ei Ra Nea 
gives the slope of the surface of 
separation between the two currents: 
1 t ue l (T-v:—T 12) 
ae eS ET) 
where tan @ is the slope of the front, 
l the deflective force due to the 
earth’s rotation, g the acceleration of 
gravity, T: and T. the temperatures 
of the two currents, and vi and v2 
the corresponding velocities. Fsom 
this formula we see that, other fac- 
tors remaining the same, the slope 
of this ideal stationary front becomes 
greater as the difference in tempera- 
ture between the two air masses (in- 
volving T.—T, in the denominator) 
becomes smaller. Also, an increas- 
ing difference in the velocities on 
either side of the front, other things 
being the same, requires an increas- 
ing slope. 
In the development of the above 
expression, several assumptions are 
made which, though probably never 
rigorously attained in Nature, are 
frequently approximated, e.g., the air 
flow on both sides of the front is 
assumed to possess no curvature. 
Slow moving fronts often approach 
this linear character. 
The conditions necessary for equili- 
brium of two air currents which are 
flowing side by side are, then, that 
the cold air must underlie the warm 
air in the form of a wedge and must 
flow, in the northern hemisphere, to 
the right of an observer looking from 
the colder into the warmer air mass. 
If, in the atmosphere, these sur- 
faces of discontinuity remained sta- 
tionary under the conditions of equi- 
librium outlined above, there would 
be little or no change in the weather, 
for weather changes are primarily 
the result of frontal movements and 
air mass interactions. Complete equi- 
librium within the earth’s atmosphere 
is never reached. In other words, 
frontal surfaces are continually 
undergoing some modification; per- 
haps they are becoming steeper, per- 
haps accelerating, or perhaps under- 
going various transformations simul- 
taneously. The reasons for these 
deviations from ideal stationary con- 
ditions are beyond the scope of this 
series of articles. It can be seen, 
however, that if a wedge of cold air 
is too steep, that is, if it exceeds 
the equilibrium value of slope given 
by (1), it will tend to flatten out, 
the colder air spreading out under- 
neath the warmer. This leads to 
vertically upward components in the 
warm air ahead of the front which, 
in turn, may lead to adiabatic cool- 
ing sufficient to form cloud. Like- 
wise, a slope which is not steep 
enough will become steeper. In this 
case a downward component is estab- 
lished within the overlying warm air. 
Once the stationary equilibrium of a 
front is disturbed so that, e.g., there 
is convergence of wind flow, the warm 
air is forced to ride over the under- 
lying cold wedge. Then most of the 
upward compenent is more likely a 
result of this convergent flow rather 
than of any change in slope of the 
front. 
Perhaps the most convenient clas- 
sification of discontinuity surfaces is 
one based upon the active or passive 
nature of the vertical component in 
the warm air above the cold wedge. 
In the active case the vertical com- 
ponent is a result of processes which 
are independent of the cold air; in 
the passive case, the moving cold air 
brings about forced vertical move- 
ments in the overlying warm air. 
In this article we shall deal solely 
with the class of discontinuities in 
which the warm air possesses an up- 
ward component of motion due to 
convergence into and ascent over an 
underlying cold wedge of air. These 
discontinuities are termed warm 
