ISENTROPIC ANALYSIS 
ing mixing ratio. We may therefore 
choose some particular surface of 
potential temperature and use the 
mixing ratio on this surface as an 
identifying element by means of which 
parcels of adiabatically moving air 
having the chosen potential tempera- 
ture may be traced from day to day. 
The equation (see Article VIII) 
S=C, log 6+ constant 
expresses the fact that a surface of 
constant potential temperature is also 
a surface of constant entropy, and 
hereafter we shall speak of it as an 
isentropic surface. Since the atmos- 
phere is normally stable, the potential 
temperature increases steadily with 
elevation. We may then consider the 
atmosphere as consisting of an infi- 
nite number of thin isentropic sheets 
limited by the surfaces 6 = constant, 
6 + d@ = constant, etc., etc. 
The above considerations, in part, 
led Rossby [2, 3] to suggest that up- 
per-air charts be drawn along isen- 
tropic surfaces, rather than along 
constant levels where the comparison 
of elements from point to point is at 
times misleading because of ascending 
and descending motion of the air 
through these level surfaces. Sir 
Napier Shaw [4] had suggested some 
years ago that weather maps be 
drawn along isentropic surfaces, and 
had actually constructed a few such 
charts containing isotherms. He 
pointed out that isotherms on an isen- 
tropic surface were also lines of 
constant density and constant pres- 
sure. But Shaw did not make use of 
the mixing ratio (w) as a second 
identifying element to be used on isen- 
tropic charts. For numerous rea- 
sons, probably the main one being the 
lack of aerological data at the time, 
Shaw’s suggestion was not put into 
practice, and the method of analyzing 
conditions along isentropic surfaces 
lay dormant until revived by Rossby 
several years later. But other consi- 
137 
derations, the fruit of later studies, 
helped to indicate that isentropic sur- 
faces should be used. 
In a study of the Gulf Stream, 
Rossby [5] found much evidence of 
large-scale cross-current mixing be- 
tween the Gulf Stream water and its 
environment, and that this mixing 
takes place along surfaces of constant 
density’. In the atmosphere, where 
compressibility must be taken into ac- 
count, it is readily seen that this type 
of mixing must operate chiefly along 
isentropic surfaces. In figure 1, for 
example, we have a normal atmos- 
pherie stratification in which the po- 
310° 
300° 
230° 
VALLIITT TELL Y/04 
WLLL 
Fic. 1. Forces RESISTING DISPLACEMENTS 
FROM ISENTROPIC SHEETS. 
tential temperature increases with 
elevation. A parcel of air originally 
resting at A, if displaced to the point 
B, will be subjected to a downward 
force F:, since it finds itself colder 
than its environment (see Art. II). 
Similarly, if the parcel is displaced to 
C a force F: resists the displacement. 
These restoring forces are propor- 
tional to the vertical gradient of 
potential temperature. But if A is 
displaced to D, that is, along an isen- 
tropic surface, there is no resisting 
force, since at each point the particle 
has the same temperature and density 
as its environment. Thus lateral mix- 
ing in the atmosphere must take place 
chiefly along the surfaces of constant 
potential temperature (isentropes). 
In saturated air the mixing operates 
2Strictly speaking, surfaces of constant po- 
tential density. 
