EXPERIMENTAL ANALOGIES TO ATMOSPHERIC MOTIONS 
tive motions were not observed, but should be the same 
as those of Fig. 5 if Vettin’s observations were accurate 
on this point (see discussion of Fig. 11 below). 
Ahlborn’s experiment [1] in 1924 consisted principally 
of rotating a small sphere, 10 cm in diameter, in a cubic 
container of water. The container was 50 cm on a side. 
The angular velocity used was about 140 rpm, which is 
a relatively high speed. The motions observed in the 
water resembled two ring vortices centered in planes 
at about twenty degrees of latitude on either side of 
the equatorial plane. Again the relative motions in 
these vortices were presumed to resemble trade-wind 
cells. But since the action is simply that of a centrifugal 
pump with frictionally duced secondary flow and 
depends essentially on having fluid brought to rest at 
the outer boundary by the box, it is quite difficult to 
see the relevance of this particular physical mechanism 
in this special form to the atmospheric problem. It is, 
of course, conceivable that frictional effects might, for 
different reasons, add up in similar ways. 
At this point some work of J. Thomson [66], which 
was outlined in his Bakerian Lecture to the Royal Society 
in 1892, may be mentioned. Thomson constructed a 
semitheoretical picture of the general circulation of the 
atmosphere in 1857, one of the earliest of the modern 
series of such attempts. This involved a meridional 
picture of a trade-wind type of cell extending from 
equator to pole aloft with a low-level cell in mid-lati- 
tudes to give the presumed average poleward drift 
in the westerlies at the surface. His interpretation of 
this cell as a secondary flow resulting from friction was 
somewhat similar to the ideas of Ahlborn but envisaged 
a more reasonable mechanism. The poleward drift in 
mid-latitudes he considered to be due to frictional re- 
duction of the speed of the low-level westerlies below 
that corresponding to balance with the pressure field 
imposed from above by the very rapid westerlies of the 
antitrades. This effect he illustrated at the lecture by 
vigorously stirring the water in a round pan and then 
observing the inward (poleward) transport at the bot- 
tom during the decay of the motion by means of parti- 
cles slightly heavier than the water. Evidently he was 
unaware of the work of Vettin, but he suggested a 
systematic series of experiments with a rotating cylin- 
drical pan, a heat source at the bottom along the outer 
rim, and a cold source near the center as one means of 
demonstrating his theory. (This is the experiment il- 
lustrated in Fig. 11 except for the lack of a strong cold 
source at the center.) So far as I have been able to 
discover, no one acted on Thomson’s suggestion until 
Exner began his work. Apparently Exner was unaware 
of Thomson’s ideas on the subject. 
In recent years, results have been obtained at the 
University of Chicago which tend to indicate that more 
intensive work of this type is worth carrying out. This 
work was begun in 1946 by the writer at the suggestion 
of Professors Rossby and Starr. Theoretical work [51] 
had suggested that the effects of lateral mixing in a 
thin spherical shell might be predominant in determining 
the gross character of the mean zonal circulations of a 
planetary atmosphere. Apparatus was constructed for 
1241 
rotating an inverted hemispherical shell of liquid of 
relatively small thickness (contained between two con- 
centric glass bowls) and for causing convective inter- 
change of the liquid between pole and equator by means 
of a heat source at the lower pole. 
These experiments have shown conclusively that sys- 
tematic relative zonal motions do occur in such a situa- 
tion (Figs. 7 and 8). Moreover, for the particular seta 
Fre. 7.—Photograph of water in the hemispherical shell ap 
paratus taken shortly after injection of two ink clouds, at 
approximately latitudes 5° and 50°, from a long hypodermic 
needle and ink tank fixed to the glass shell. An electric heating 
element is located at the pole. (Rate of rotation is 8.18 rpm, 
heating at 20 v, mean radius of shell 10 cm, thickness of space 
containing water 1.6 cm, rotation is from right to left as seen.) 
(After Fultz [22].) 
of conditions so far investigated, if these relative mo- 
tions are represented nondimensionally as ratios of 
relative speed u to the absolute speed Cz of a point 
Pics ep 
Fie. 8.—Photograph taken 14.6 see after Fig. 7. For 10 
latitude u/C, is close to +0.016, while for 50° latitude it is 
close to —0.036 (cf. Fig. 7). (After Fultz [22].) 
fixed on the equator of the bowls, they have values 
ranging up to 0.15.* This is just the order of magnitude 
of such ratios in the earth’s atmosphere where Cx is 
about 1000 mph. Also, as shown in Fig. 9, even the 
4. This ratio u/Cp = u/rQ is apparently an even more im- 
portant similarity parameter than is indicated by its kinema- 
tic significance as a velocity ratio. In the form Qu/r it is a 
ratio of a characteristic Coriolis force to a characteristic cen- 
trifugal force (except for the unimportant numerical factor). 
In the form (u?/r)(1/Qu) it is a ratio of a characteristic rela- 
