34 AIR MASS ANALYSIS 
the front—bulges in the line of the 
discontinuity. The origin of these 
waves is to be sought in the factors 
which, acting together, determine the 
equilibrium of the frontal surface. 
An upset of this equilibrium at some 
section of the front may readily 
develop into a wave.* 
In Fig. 8 (a) the Polar Front is 
shown before the beginning of a wave 
disturbance. Arrows represent the 
air flow; (b) shows the formation of 
a bulge in the front which is the 
start of a wave. The stippled area 
indicates where precipitation is fall- 
ing. In this case it is the result of 
the vertical displacement of the trop- 
ical air over the cold underlying 
wedge. In the final analysis this is 
due to the disturbance of equili- 
brium. There are now two possi- 
bilities: the wave may travel along 
the front and remain a wave disturb- 
ance, later flattening out and dying; 
or, as it moves, it may increase in 
amplitude to such an extent that one 
side of it overtakes the other. This 
question of the stability of the wave 
cannot be treated in any detail here. 
Most of the disturbances which re- 
main as waves along a front are those 
of small amplitude and short length. 
Longer waves of relatively large am- 
plitude tend to close up—the coid 
air completely displacing the warm 
air from the surface. 
The movement of these waves, ac- 
cording to V. Bjerknes, is the vector 
resultant of two components (Fig. 12) : 
(1) the dynamic component of the vel- 
ocity due to the displacement of the 
wave motion along the boundary sur- 
face and (2) the movement of the 
medium itself (the air in the vicinity 
of the front). Thus the -forecasting 
of the motion of these waves is based 
upon an estimate of the mean result- 
ant velocity of the air currents in 
the frontal region and an estimate 
of the translational velocity of the 
wave itself (i.e., the velocity it would 
have in the event the mean resultant 
velocity were zero). In this connec- 
tion it is well to note that the com- 
ponent of translation due to the wave 
motion in the medium cbeys the gen- 
eral physical laws of wave motion, 
i.e., flat, long waves travel rapidly 
compared to waves of large ampli- 
tude. It may also be shown that, in 
the northern hemisphere, the com- 
ponent of velocity due to the wave 
motion itself must be so directed that 
the wave moves to the right of an 
observer looking from the warm into 
the cold air. If the mean velocity of 
the interacting air currents also pos- 
sesses this direction, it is clear that 
the wave will travel rapidly. On the 
other hand, if the resultant velocity 
of the air currents is directed op- 
posite to the component due to tne 
wave motion, the wave will move 
slowly, or it may even be fairly sta- 
tionary. In the United States tne 
wave component of the velocity is of 
more importance, for here the fronts 
frequently have a NE-SW direction 
and the cold NE current generally 
falls off rapidly with elevation. In 
the United States, then, the normal 
movement of wave disturbances is in 
a general easterly or northeasterly 
direction. (See Fig. 12.) 
If the wave continually increases 
in amplitude its successive stages are 
represented in fig. 8 by (c), (d), (e), 
and (f). In these diagrams the solid 
heavy lines represent cold fronts; the 
double light lines, warm fronts; the 
broken heavy lines, occluded fronts 
(defined below); and the light solid 
lines, isobars. Stippled areas show 
where precipitation is falling. The 
right-hand section of the wave be- 
*The theory of this is explained in the 
article by Haurwitz following this chapter. 
