EXTRATROPICAL CYCLONES 
By J. BJERKNES 
University of California, Los Angeles 
With the consent of the editor the present article 
has been written as a summary of the research on 
extratropical cyclones in which the author himself has 
been directly involved. References to the work of others 
are therefore few, and the reader will not get a com- 
plete survey of the title subject. 
This article is composed of two parts. In the first, 
extratropical cyclones are treated as simplified models 
for the sake of clarifying the theoretical principles. 
In the second, these principles are applied to a real 
storm over North America whose development may be 
considered as the prototype of a simple life history of 
extratropical cyclones. The modifications of that life 
history, caused by the varying initial conditions and 
the influence of neighboring systems in the general 
circulation, are treated by Dr. E. Palmén in his con- 
tribution to the Compendium. 
DYNAMICS OF SIMPLIFIED CYCLONE 
MODELS 
Theory of Pressure Changes and Thermal Structure 
of Extratropical Cyclones. The fully developed extra- 
tropical cyclone consists of a counterclockwise! vortex 
which extends upward into a wave trough in the upper 
westerlies. The dynamics of the extratropical cyclone 
is therefore a composite one, combining the dynamic 
phenomena of the vortex and the wave. We will here 
state separately the essential features of the atmos- 
pheric vortex and the atmospheric wave and then 
proceed to describe the composite dynamics of the 
extratropical cyclone. 
In analyzing the displacement, intensification, and 
weakening of vortices and waves it is useful to con- 
sider the accompanying pressure changes, which obey 
the ‘‘tendency equation,” 
(2) ul 
ot h 
Expressed in words, the rate of pressure change with 
time at a fixed point at the level h is determined partly 
by the net horizontal inflow into the vertical unit air 
column from h to the top of the atmosphere and partly 
by the vertical inflow of air through the base of that 
column. 
A circular cyclonic vortex with vertical axis centered 
at the pole of a planet without mountains represents 
the simplest case of atmospheric vortex dynamics. In 
the case of frictionless motion in such a polar vortex 
the particles could be kept in steady-state zonal motion 
from west to east. The horizontal divergence is then 
i" [ osive (pv)dz + (goven. (1) 
1. All references to the sense of rotation in this article 
apply to the Northern Hemisphere. 
everywhere zero and no vertical motion occurs, so that 
the tendency equation must indicate zero local pres- 
sure change at all pomts. With friction against the 
ground, the flow in the lowest part of the atmosphere 
would be given a component of indraft towards the 
vortex center, and this horizontal convergence of mass 
would make the pressure rise in the central portion of 
the pressure minimum, thus decreasing the zonal air 
motion. No steady state would be reached until the 
flow at the ground and the horizontal pressure gradient 
at the ground have reached zero. If the central core 
of the vortex is colder than its environment, there would 
still be a pressure gradient towards the pole in the 
free atmosphere, and there the air may continue its 
west to east circulation without horizontal divergence. 
This picture corresponds rather well to reality as repre- 
sented by the time-averaged motion in the arctic region: 
almost zero meridional pressure gradient and zero zonal 
motion at the ground, and increasing poleward pressure 
gradient with height, accompanied by increasing 
westerlies with height. The initial assumption of a 
cyclone at the pole, and the additional assumption of 
friction at the ground, thus lead to the dynamical 
prediction that the cyclone at the ground should even- 
tually disappear, while in the free atmosphere it should 
be conserved. This behavior of the circular cyclonic 
vortex can be generalized to apply also at other lati- 
tudes; the simple circular vortex is liable to die out 
gradually at the ground because of friction. 
The circular cyclonic vortex centered in middle lati- 
tudes does not represent a steady-state dynamic sys- 
tem even in the absence of friction at the ground. 
Although the horizontal pressure gradient may every- 
where be directed towards the center and its intensity 
may be a function only of the distance from the center, 
the motion around the center cannot be a simple 
circular one, because the Coriolis parameter varies 
from the northern to the southern part of the vortex. 
As a result of the variation of the Coriolis parameter 
the wind will be stronger in the southern than in the 
northern part of the vortex, and the net air transport 
across a north-south median wall will be from the 
western to the eastern half of the vortex. Consequently 
the pressure will rise in the eastern half because of 
horizontal convergence and fall in the western half of 
the low pressure system because of horizontal diver- 
gence, so that the pressure minimum and the accom- 
panying vortex will drift westward. Eccentricity of 
the pressure field of such a sense as to involve a stronger 
pressure gradient in the southern than in the northern 
part of the vortex may reduce, neutralize, or even 
reverse that drift. The dynamic theory for the ec- 
centric vortex has been developed in approximate form 
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