THE METHOD OF CHARACTERISTICS 
can then be studied in the x, y plane like equations (1) 
and (2). This equation is complicated by the fact that 
real characteristics exist only under certain conditions, 
that is, if 
7 
w+ v2 > gh (: - S) (35) 
The study of steady-state flows has not been applied 
in synoptic meteorology to date. The only published 
discussions of a steady two-dimensional flow are the 
climatological example in the next paragraph and the 
conjecture of Tepper discussed below [19]. 
An Example of a Two-Dimensional Steady Flow. An 
example of the type of flow described in the previous 
section has been given by Freeman [9]. The chart from 
the Climatic Charts of the Oceans [22] showing mean 
resultant winds off the west coast of South America in 
October is reproduced in Fig. 14. This is to be compared 
SOUTH 
AMERICA 
10°S 
20°S 
1N0°W 90°w 80°wW 70°w 
Fic. 14—The resultant wind field east of South America 
in October from the Climatic Charts of the Oceans. The dashed 
lines are isopleths of Beaufort force. 
to the Prandtl-Meyer type of expansion wave in Fig. 
15. This expansion wave is computed from the following 
initial data: Winds of 5 m sec! (force 3) under an in- 
version of 1C at 0.65 km are blowing parallel to the 
coast of South America and pass the bend in the coast 
line. The wind speed is assumed to be somewhat higher 
than the observed surface wind to allow for slowing by 
surface friction. The height and strength of the inver- 
sion is that found by Alpert [2]. Points of similarity of 
these flows are that the change in wind direction occurs 
farther north as the longitude increases and that the 
winds increase their speed as they turn around the 
corner. The slowing down of the resultant winds north 
of 5°N is to be expected because the expansion wave 
does not always extend to that latitude and when it 
does it is more likely to be modified by the Northern 
Hemisphere wind systems. This may not be the only 
431 
factor causing these winds, but it must certainly be an 
important one, since the data fit the theoretical model 
so well. 
10°N 
AMERICA 
10°S 
20°S 
100°w 80°W 70°W 
_ Fic. 15.—The computed wind field if the air under an 
inversion undergoes a Prandtl-Meyer expansion around the 
bend in the west coast of South America. 
90°W 
Interaction of Two Pressure-Jump Lines. It has been 
proposed by Tepper [20] that the intersection of two 
pressure-jump lines should be a region of preferred 
occurrence of tornadoes. He cited the discussion of 
interactions by Courant and Friedrichs [5] to lend 
support to this conjecture. When two shock waves 
intersect in the two-dimensional flow of a compressible 
fluid a vortex sheet is formed. This vortex sheet has 
been found experimentally in gas flows and in flow of 
water in a channel. Such a vertical vortex sheet should 
form behind the intersection of two pressure jumps. If 
the circular properties of a tornado are similar to those 
of the dust devils studied by N. R. Williams [24], then 
such a region of strong shear is a very likely zone for 
tornado formation. 
Tepper [20] found that, in five out of the seven tornado 
situations he studied, the tornadoes formed within fifty 
miles of the intersection of two pressure jumps. 
CURRENT PROBLEMS AND SUGGESTIONS 
FOR RESEARCH 
The application of the method of characteristics to 
meteorological problems is an active field of research 
with many topics of interest. Most of the problems 
under consideration at the present time are concerned 
with flow under an inversion. The path to follow in the 
solution of many of these problems is clearly marked. 
Other problems are being attacked with success by 
Tepper. The success of Abdullah [1! in explaining the 
“secondary cold front”? or ‘‘postfrontal squall line’”’ and 
of Tepper in explaining the occurrence of the “squall 
line” indicates that many phenomena on the same and 
smaller scales can be studied with this theory in mind. 
