EXPERIMENTAL ANALOGIES TO ATMOSPHERIC MOTIONS 
2. The work of Fultz [22] should be extended to 
spherical shells incorporating variable depth-radius ra- 
tios which Rossby’s theory would imply to be im- 
portant. The data from these experiments need to 
include much more complete temperature values and 
also more extensive velocity observations. By use of 
the rotoscope and appropriate mirror or lens systems 
it will be possible to obtain velocity values much more 
easily and accurately. With enough data to be sta- 
tistically significant, it will be possible to calculate 
such properties of the motion as the horizontal Rey- 
nolds’ stresses (momentum transfers). The data taken 
in 1947 have been found insufficient to give reliable 
estimates of such secondary quantities. 
3. A most important companion set of experiments 
to these spherical shell studies needs to be carried out 
in paraboloidal shells rotated at rates such that the 
free surface figure coincides with that of the parabo- 
loid.2 All the previous types of work should be carried 
out here. An even better check on the Jeffreys comment 
above would be obtained by comparing a cold-pole— 
Wwarm-rim setup with a warm-pole—cold-rm. With 
a moderately deep layer it should be possible to com- 
pare the efficacy of heat sources at high altitudes and 
cold sources at low altitudes with the opposite case in a 
way that would have relatively conclusive application 
to the controversy mentioned earlier. 
There is one caution here that a rough calculation 
brings up. If we consider the thermal expansion of 
water (or most other practicable liquids) and ordinarily 
available temperature gradients, it appears that the 
thermally developed horizontal pressure-gradient forces 
are likely to be of a very small order relative to gravity. 
If these forces are not to be masked by inaccuracies of 
figure (which would give rise to components of the 
external action along the surface), the paraboloid may 
need to have a slope at each radius accurate to 10° 
parts or better. Corresponding requirements would sub- 
sist for the constancy of angular velocity of the basic 
rotation. Such accuracy will be very difficult to obtain 
practically. There may be means of handling the situa- 
tion without proceeding to this degree of precision, but 
some experience and trial and error will be needed to 
work them out. 
4. Shearing waves and instability at density discon- 
tinuity surfaces in general deserve extensive investiga- 
tion, in both the rotating and nonrotating cases with 
various geometrical forms (see, for example, Keulegan 
[87]). Here the problem of obtaining velocity measure- 
ments of the required density and accuracy for meteo- 
rological application is very serious. But, at least in 
the case of liquids, modifications of the standard aero- 
dynamic aluminum-powder techniques using sparser 
distributions (or possibly liquid bubble tracers) with 
rapid-sequence flash photography should be valuable. 
In all of the cases mentioned above there are many 
conclusions concerning these experiments as quite provisional. 
They will be discussed as comprehensively as possible in an 
early publication on this aspect of our work. 
9. This was first brought to my attention in this connection 
by the group at the University of California at Los Angeles. 
1245 
obvious extensions such as (a) varying the contour and 
roughness of the underlying surfaces, for example. 
mountain barriers or other forced depth changes, (6) 
studying the motions of thermally irduced currents 
around obstacles of various shapes or moving the ob- 
stacles themselves through the fluid with and without 
concomitant convective motions (see [26] and [24]), 
and (c) studying the effect of a varying horizontal 
conductivity of the underlying surface on convective 
motions, for example, ocean versus land differences of 
this kind. 
Concerning smaller-scale problems it appears that 
important work could be done on vortices (tornadoes 
and hurricanes) by careful measurements of field quan- 
tities around one or the other of the experimental 
cases. Probably the simplest would be one of the steady 
mechanically driven air vortices such as Weyher’s. Ve- 
locities could be obtained by a series of probes with a 
microsized Pitot tube or hot-wire anemometer. The 
vexing problem of just how much weight to attach to 
all the reasoning concerning “‘vr’’ vortices and momen- 
tum conservation in these circumstances should receive 
some elucidation. Projected experiments of other types 
have been referred to earlier. 
There exist at least two fields in which the possibili- 
ties of significant experimentation seem very large and 
which, from the meteorological angle, are just opening 
up at the present time. One of these is the field of hy- 
draulic and supersonic gas flow analogies, opened for 
meteorology by Freeman [20]. Current work by Rossby 
indicates that there may exist even larger-scale analo- 
gies to the hydraulic jump than those considered by 
Freeman and later workers. Quite aside from the de- 
sirability of modifying the extensive experiments which 
have been carried out in this field so as to lay special 
stress on: the meteorologically important quantities, 
there is every prospect that significant amounts of 
rotation can be introduced experimentally. For ex- 
ample, a small version of the complete table described 
by Matthews [46] could rather easily be arranged so as 
to be rotatable. Similar open-channel work with sub- 
critical flow has in fact already been done in the rotating 
room at Géttingen by Fette [18]. 
The second field is one in which hardly anything of 
meteorological significance has yet been done experi- 
mentally, but in which many possibilities must exist. 
This area is that of electromagnetic analogies. Such 
analogies have quite often been used in potential flow 
problems where a direct electrical analogy in conducting 
fluids is very easy to apply in practical problems for 
which the boundaries are complicated [39, p. 65). 
An extensive discussion of another sort of identity 
between electromagnetic and hydrodynamic systems 
(with experimental illustrations) has been given by V. 
Bjerknes [9]. Another has been interestingly pointed 
out and used by Ising [84]. In this paper, advantage is 
taken of the fact that there is complete identity in 
form between the equations for an incompressible fluid 
in the usual meteorological relative coordinate system 
rotating at a constant angular velocity and those for a 
corresponding system of electric currents in a uniform 
