Abstract Previous studies of the long-wave perturbations of the free atmosphere have been based on mathematical models which either fail to take properly into account the continuous vertical shear in the zonal current or else neglect the variations of the vertical component of the earth's angular velocity. The present treatment attempts to supply both these elements and thereby to lead to a solution more nearly in accord with the observed behavior of the atmosphere. By eliminating from consideration at the outset the meteorologically unimportant acoustic and shearing-gravitational oscillations, the perturbation equations are reduced to a system whose solution is readily obtained. Exact stability criteria are deduced, and it is shown that the instability increases with shear, lapse rate, and latitude, and decreases with wave length. Application of the criteria to the seasonal averages of zonal wind suggests that the westerlies of middle latitudes are a seat of constant dynamic instability. The unstable wav...
[1]
B. Gutenberg,et al.
Physical Properties of the Atmosphere up to 100 km
,
1946
.
[2]
Edmund Taylor Whittaker,et al.
A Course of Modern Analysis
,
2021
.
[3]
W. J. Archibald.
XXXVIII. The complete solution of the differential equation for the confluent hypergeometric function
,
1938
.
[4]
J. Bjerknes,et al.
ON THE THEORY OF CYCLONES
,
1944
.
[5]
T. Bergeron,et al.
Physikalische Hydrodynamik: Mit Anwendung auf die Dynamische Meteorologie
,
1933
.
[6]
C. Rossby.
Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action
,
1939
.