MODEL TECHNIQUES IN METEOROLOGICAL RESEARCH 
By HUNTER ROUSE 
Towa Institute of Hydraulic Research, State University of Iowa 
Introduction 
Scale-model investigations of fluid motion have long 
since proved their worth in such widely varied fields as 
aeronautics, ballistics, hydraulics, and naval archi- 
tecture. New aircraft, projectiles, turbines, spillways, 
and ships are almost invariably tested at reduced scale 
before final acceptance of design, and prototype be- 
havior is being predicted with ever-increasing accuracy. 
Particularly in the field of flood control and river regula- 
tion, economies of construction: or improvements in 
design which model studies generally reveal have offset 
the costs of the studies many times over. It is therefore 
hardly surprising that meteorologists frequently wonder 
whether model techniques would not be useful in mete- 
orological research as well. 
Wind-tunnel studies of meteorological phenomena 
have, in fact, already been described in the literature 
on at least a dozen occasions, a card file of such papers 
being maintained by the U.S. Weather Bureau. During 
World War II, moreover, a considerable number of 
model investigations were made of particular atmos- 
pheric occurrences, although many of the results have 
not yet been published. Each project of this nature was 
undertaken for the specific reasons behind all laboratory 
research at small scale: on the one hand, the essential 
variables can be controlled at will; on the other hand, 
small-scale experimentation generally reduces to an 
extreme degree the time and expense involved. It is 
true, of course, that few large-scale occurrences can be 
reproduced to perfection in a laboratory model, while 
some—such as those of the atmosphere as a whole—are 
so complex that their duplication i miniature would 
be utterly impossible. Nevertheless, many flow phe- 
nomena become subject to analysis only when reduced 
to their bare essentials, and hence even a very rough 
approximation of actual conditions is often fully justi- 
fied. 
If model studies are to provide useful prototype indi- 
cations, the followig steps are generally necessary in 
addition to the actual tests. First of all, a preliminary 
analysis of the problem should be made, based upon 
dimensional considerations and such physical prin- 
ciples as are readily applicable, so that the subsequent 
experiments may be efficiently conducted. Secondly, 
the experiments should be planned to make optimum 
use of available equipment and instruments, or suitable 
apparatus must be devised. Finally, the results of the 
experiments should be reduced to their most general 
form for utilization at prototype scale. In the following 
pages each of these aspects of model technique is dis- 
cussed in detail with particular application to meteoro- 
logical research, and typical problems already investi- 
gated by such means are described. 
Similitude Requirements 
A very powerful tool of laboratory research is the 
procedure known as dimensional analysis [3]. Frequently 
maligned by some because of its limitations and fre- 
quently misused by others who do not recognize its 
limitations, the method is actually of great worth as a 
systematic guide and check in planning new experi- 
mental studies. Based upon the physical requirement 
of dimensional homogeneity in any functional relation- 
ship, such analysis permits the variables involved to be 
reduced in number, generalized in form, and brought 
into an arrangement suitable for experimental inves- 
tigation. 
The Il-theorem [4] of dimensional analysis states that 
if the n variables involved in a function require m di- 
mensional categories for their expression, then the func- 
tion can be rewritten in terms of n — m dimensionless 
groups of these variables. Moreover, this theorem pro- 
vides a systematic algebraic procedure whereby any 
series of variables involved in a phenomenon, regardless 
of their number or the number of the dimensional 
categories, may be reduced to a significant dimension- 
less form. Here it is sufficient to say that any problem 
of geometry alone will thus be expressible in terms of 
ratios of lengths, and that model and prototype boun- 
daries and flow patterns will be geometrically similar if 
all corresponding length ratios have the same numerical 
value in both cases. Likewise, a problem of kinematics 
will be expressible in terms of ratios of lengths and times 
—or combinations thereof, such as velocities—and 
hence model and prototype occurrences will also be 
kinematically similar if all corresponding kinematic 
ratios are identical. Finally (at least so far as phenomena 
of mechanics are concerned), a problem of dynamics will 
be expressible in terms of ratios of quantities involving 
length, time, and either force or mass; accordingly, 
model and prototype occurrences will be dynamically 
similar as well if all corresponding dynamic ratios are 
the same in both. 
The various quantities required to describe any phe- 
nomenon of fluid mechanics include a series of lengths 
a, b, c,... descriptive of the boundary geometry; a 
series of flow characteristics such as velocity V and 
differential pressure Ap; and a series of fluid properties 
—the density p, the differential specific weight Ay, 
the dynamic viscosity p», and the bulk modulus of 
elasticity e. Although many different dimensionless ar- 
rangements of these variables may be obtained by the 
II-theorem, the following is most significant for con- 
ditions of similarity [14]: 
V u G c Vv Va V ) 
/2Ap/p  * \a’ a’? V/ady/p’ u/p’ Ve/p/]” 
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