NORWEGIAN WAVE-THEORY 
Al 
Thus the displaced particle has a 
deficit of centrifugal force which 
drives it back to its original position 
where it is in equilibrium with its 
surroundings. Similarly when a parti- 
cle is displaced towards the axis it 
obtains a surplus of centrifugal force 
as compared to the surrounding fluid 
and will again move towards its ini- 
tial position. Thus the origin of iner- 
tia waves is easily understood. If a 
particle is displaced outwards from 
its equilibrium position it is driven 
back to this position. But while mov- 
ing back to the equilibrium position 
it acquires kinetic energy so that it 
approaches the axis of rotation more 
closely than before the disturbance 
until the surplus of centrifugal force 
which the particle gains in approach- 
ing the axis overcomes the kinetic 
energy and reverses the direction of 
motion again. The process is com- 
pletely analogous to the wave motion 
in the atmosphere in stable equili- 
brium, except that there the deficit 
or surplus in weight as compared to 
the surrounding air plays the role of 
the centrifugal force. 
EARTH’S ROTATION 
It is obvious from the previous 
considerations that inertia waves in 
a fluid rotating with constant angu- 
lar velocity are stable. If our atmos- 
phere were at rest with respect to 
the surface of the earth, it would 
appear to an extra-terrestrial observer 
to rotate with constant angular velo- 
city around the earth’s axis. In real- 
ity, owing to the different winds in 
the atmosphere, or, in other words, 
to atmospheric motions relative to 
the earth, the atmosphere does not 
have strictly speaking a constant 
angular velocity. However, closer 
inspection shows that the wind dis- 
tribution in the atmosphere is such 
that inertia waves of the dimensions 
of cyclonic waves are alwavs stable. 
With Bjerknes and Godske*) we may 
call this the “dynamic stability” due 
to the earth’s rotation, while the 
stability of the gravitational waves 
in the earth’s atmosphere might be 
termed “static stability”. 
Another important effect of the 
earth’s rotation is the following. In 
purely gravitational waves the motion 
of the fluid particles takes place in a 
vertical plane, for the direction of 
the gravitational force is vertical. The 
deflecting force of the earth’s rota- 
tion, on the other hand, acts perpen- 
dicular to the earth’s axis. Thus it 
acts purely vertically only at the equa- 
tor. At the pole it is directed hori- 
zontally, but at all other latitudes it 
is inclined to the horizon, so that we 
can speak of a horizontal and a verti- 
cal component. The vertical compo- 
nent generally can be neglected in 
meteorology since its direction coin- 
cides with the far greater accelera- 
tion of gravity. The horizontal com- 
ponent of the deflecting force of the 
earth’s rotation causes an inclination 
of the plane of motion with respect to 
the vertical. The inclination is larger 
the greater the motion; thus in the 
long cyclonic waves the motion is 
predominantly horizontal, while in 
the small billow clouds it is vertical. 
CYCLONIC WAVES 
Now that the different factors 
which cause and influence wave mo- 
tion have been considered separately 
it can more easily be understood how 
they act together to produce the cy- 
clonic waves. 
It was stated that according to the 
Norwegian wave theory we have 
frontal surfaces between air masses 
of different density (temperature, 
moisture content). Due to the differ- 
ent densities on opposite sides of the 
*Bjerknes, J.; and Godske, C. L.: On the 
theory of cyclone formation at extra-tropical 
fronts, Astrophysica Norvegica, Vol. I. no. 6, 
1936, pp. 218-219. 
