584 
under the straight southwesterly currents of long waves, 
and for a study of these phenomena we will here con- 
sider the theory of adiabatic, mertial motion in tilting, 
stationary isentropic surfaces. Adiabatic (or pseudo- 
adiabatic) changes of state of particles in the free 
atmosphere can justifiably be assumed, because non- 
adiabatic temperature changes are so slow and uni- 
formly distributed that they do not appreciably affect 
a relatively rapid phenomenon such as cyclogenesis. 
+7 
ta) 
Fig. 6.—Profile of sloping isentropic x7-plane and sample dis- 
tribution of the isovels of vg in rn-coordinates. 
The followimg simplified analysis has been inspired 
by the theoretical studies on “dynamic instability,” 
which go back to the classical paper of Helmholtz, 
“Uber atmospharische Bewegungen,” published in 1888 
[12]. Several recent contributions by theoretical meteor- 
ologists to the same field have been included in the list 
of literature references [6-9, 14, 15, 17-19, 21, 31, 32]. 
The synoptic applications of equation (11) in this 
article to the problems of frontogenesis and cyclogenesis 
have, to my knowledge, not been attempted before. 
The adiabatic movement of a particle parallel to an 
isentropic surface (sloping or horizontal) is not opposed 
by buoyancy forces and is left to the stable or unstable 
control of the horizontal pressure gradient and the 
Coriolis force. The same is true for particles of entire 
isentropic sheets moving in unison, when they are far 
enough from the ground to be independent of boundary 
effects. For the purpose of this article we shall consider 
the environmental field of pressure and potential tem- 
perature constant while the sample particle (or sample 
isentropic sheet) moves isentropically through the field. 
We shall consider part of an isentropic surface of 
MECHANICS OF PRESSURE SYSTEMS 
sufficiently small extent to be treated as a sloping plane 
(Fig. 6), on which the horizontal direction will be called 
the «z-direction (due eastward) and the direction of 
steepest slope (due northward) will be called the 7- 
direction. The 7-axis is supposed to form an angle with 
the horizontal y-axis of the order of one in a hundred or 
less. The undisturbed air motion is supposed to be 
zonal, geostrophic, and horizontal, which allows the 
isentropic surface to stay fixed in space. Furthermore 
the fundamental motion is constant along each stream- 
line, dv,/dx = 0, and represents a steady state, dv./dt = 
0. Later application to the long wave, where the quasi- 
straight flow is not exactly zonal, will be done without 
any strict mathematical treatment. The disturbed 
motion of the sample particle is supposed to be con- 
tained in the isentropic surface and to have an initial 
upslope component v, superimposed on the general 
horizontal motion characteristic of the environment. 
The x-component of acceleration of the disturbed 
particle amounts to 
& = 20).0,, 2-0, (7) 
and makes the particle speed up in the positive z- 
direction while it climbs the isentropic slope. The wind 
of the environment v, , which is geostrophic and directed 
along the z-axis in the whole field, changes in value 
along the path of climb. An observer following the 
disturbed particle would see the environmental geo- 
strophic wind, relative to the earth, change by 
dig _ Og 
rie Vn ai : (8) 
The z-component of the speed of the disturbed particle 
was assumed to be equal to the geostrophic wind v, at 
the initial time. Depending on whether dv./dt > dv,/dt 
or dv,/dt < dv,/dt, the disturbed particle will move 
eastwards faster or slower than its new environment 
after a time differential of climbing. In the first case, 
the y-component of acceleration of the disturbed par- 
ticle dv,/di = —2Q(v, — vz) will be directed down the 
isentropic slope opposite to the initial disturbance. 
A stable inertia type of oscillation will then result. In 
the second case, the y-component of acceleration will 
point in the same direction as the initial disturbance 
velocity v, , so that an exponential growth of the dis- 
turbance will follow. The instability case is thus 
dv,z/dt < dv,/dt. In order to make the instability cri- 
terion applicable also for the downward directed dis- 
dvs dv, 
dt dt 
Now, provided that the substitution of v, for v, in 
(7) is justified by a sufficiently small inclination of the 
isentropic surface, the instability criterion derived from 
(7) and (8) takes the simple form, 
turbance, it should be written < 
Sen OO Te (9) 
The observed increase of westerly geostrophic wind 
from the lower to the higher portion of an isentropic 
