EXPERIMENTAL ANALOGIES TO ATMOSPHERIC MOTIONS 
By DAVE FULTZ 
University of Chicago 
Introduction 
One of the very old dreams of meteorologists and 
other scientific observers who have concerned them- 
selves with the phenomena of the atmosphere has been 
that of solving some problems (as many as possible, of 
course) by means of experimental work on a small 
scale. In view of the difficulties of purely theoretical 
approaches and of interpreting the uncontrollable varia- 
tions of the actual atmosphere, many have had hopes 
of obtaming valuable results and insights from such 
experiments as a supplement to, and a source of, theo- 
retical ideas. Typical statements of such views are those 
of Schmidt [56, p. 1135] and Richardson [89]. In recent 
times the increasingly far-reaching successes of model 
experimentation in aerodynamics, hydraulics, oceanog- 
raphy, and other fields have given renewed impetus 
to efforts at serious work on meteorological questions 
by this means. 
There are many serious difficulties in the application 
of model techniques, as they have been developed in 
other fields, to the study of such a complex system as 
the atmosphere.! Particularly in the medium- and large- 
scale aspects of atmospheric motions, so many factors 
are involved that a straightforward dynamic-similarity 
analysis of the usual kind leads inevitably to the con- 
clusion that, within practical limitations, the model 
must be identical with the prototype. The choice of real 
fluids available for experimentation, the serious in- 
conveniences connected with the presence of gravity, 
and many other factors made this conclusion unavoid- 
able. Basically, therefore, any model experimentation 
that aims at real resemblance to the atmosphere of a 
planet and thence to the discovery of principles govern- 
ing phenomena in such atmospheres, will have to accept 
deliberate distortions of certain kinds and will have to 
intercompare many partial types of experiments and 
analyses in the effort to arrive at valid conclusions 
concerning the operation of these principles. In this 
respect the situation is similar to, though more compli- 
cated than, that which is encountered in sedimentation 
studies on river models. 
I hope in the succeeding parts of this paper to review 
briefly some of the rather considerable amount of ex- 
perimental work of various types which has been done 
with the atmospheric problem more or less in mind, 
to mention some of the reasons for expecting a renewed 
and vigorous attack on this area to be more profitable 
in the future than it was in the past, and to suggest some 
immediate directions along which such an attack might 
develop. With some exceptions, the topics to be dis- 
cussed will be restricted to problems concerned with 
1. Consult ‘Model Techniquesin Meteorological Research” 
by H. Rouse, pp. 1249-1254 in this Compendium. 
relatively large-scale motions, such as cyclones or the 
general circulation. Experimental work on certain small- 
scale phenomena, such as convectional layers and flow 
in the friction layer, are discussed by D. Brunt? and 
H. Rouse.? 
General Considerations 
In the problem of the atmosphere as a hydrodynamic 
fluid we are concerned essentially with these factors: 
1. Strong effects of rotation. 
2. Thermodynamic activity or “convection” as an 
important ultimate driving mechanism and probably the 
only one of real significance. 
3. Primary effects of ‘friction’? mm one sense or 
another. 
4. Important alterations brought about in the opera- 
tion of all the preceding factors by the great horizontal 
extent of the atmosphere relative to its vertical extent. 
The last factor, perhaps more than any of the others 
except rotation, fixes the specific character of an atmos- 
pheric motion and must somehow be dealt with in the 
interpretation of experiments. Since these factors are 
inextricably combined with other dynamic factors which 
are more fully understood and more completely ana- 
lyzed, the task of disentangling them and assigning 
each to its proper place is formidable. 
In an experimental approach, which must of course 
be guided as closely as possible by theory and observa- 
tion, a more than ordinary amount of groping will be 
inevitable. Similarity analyses need to be made but, 
for example, even the significance of Il-terms such as 
g/a®, where g is the acceleration of gravity, a is the 
radius of the experimental sphere or a planet, and Q 
is the angular velocity of the sphere, is not the same in 
the heating experiments in a thin spherical shell re- 
ported by Fultz [22] (and discussed below) as for the 
planet. In the planetary case, g is the intensity of a 
central force, and the solid surface is an equipotential 
surface for gravity plus the centrifugal force. In the 
experiments mentioned above, g refers to the intensity of 
a uniform field of force, and the spherical surface is not 
an equipotential surface. In spite of this and other 
differences, kinematic similarities at least did appear 
in these experiments; furthermore, there are qualita- 
tive theoretical reasons for expecting this to be so. Thus 
the fact that kinematic similarities were found is not 
likely to be mere coincidence. 
It would be foolish to expect these similarities to 
extend to every aspect of the dynamics of these two 
systems. But it is not unreasonable to expect similarity 
in some predominant, basic mechanism. As suggested 
2. Consult ‘‘Experimental Cloud Formation” by D. Brunt, 
pp. 1255-1262 in this Compendium. 
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