MODEL TECHNIQUES IN METEOROLOGICAL RESEARCH 
thereof) was essentially independent of the Reynolds 
number. Measurements of gas concentration c could 
therefore be reduced to generalized nondimensional 
contours of relative concentration cV L?/Q, in which Q 
is the rate of gas release, V the mean air speed, and L 
a characteristic building dimension, as shown sche- 
matically in Fig. 1. Similar techniques are evidently 
applicable to studies of smoke abatement, the dis- 
persion of radioactive by-products, or—at least quali- 
tatively—the mixing of moisture-laden air in moun- 
tainous terrain. 
Two somewhat allied phenomena of the atmosphere 
are impossible to reproduce quantitatively to scale in 
the laboratory, yet they involve complexities which 
are so great that even the qualitative laboratory simula- 
tion of their primary characteristics is often useful. 
One of these is the effect of the earth’s rotation, and the 
other the effect of thermal stratification. Since the 
accelerative forces due to rotation of the flow system 
as a whole cannot well be included in a general model, 
it 1s usually necessary [13] to reproduce the effect in a 
rotating tank at very small scale, as is described else- 
where in this volume,! or—as is sometimes done—in a 
small rotating room. At such scale, of course, viscous 
action plays a role which is wholly out of proportion 
to that of any prototype condition, and the indications 
must be interpreted in the light of the mechanics of 
viscous flow. Although studies of this nature generally 
involve thermal (or density) stratification of the fluid 
[7], other stratification phenomena warrant detailed 
study in their own right. These, in fact, are of interest 
to a number of professions (oceanography, harbor hy- 
draulies, and sedimentation), and have often been re- 
produced in the laboratory [2]. 
For purposes of convenience, studies of this nature 
are usually conducted in water, the density stratifica- 
tion being obtained by means of saline solutions of 
various concentrations. This technique has permitted 
the study of (1) wave motion at and mixing across a 
density interface, (2) the progress of sediment under- 
flow (comparable to a dust cloud or even a cold front) 
through a reservoir, and even (8) the effect of a sche- 
matic mountain range upon successively higher thermal 
zones of the atmosphere. Under certain conditions, to 
be sure, viscosity plays a role which is quite out of 
keeping with prototype conditions, and thermal ef- 
fects other than that of the density differential cannot 
be reproduced. However, so long as the interrelation- 
ship between gravitational action and mass reaction is 
the primary factor involved, model studies of this 
‘ nature can be expected to yield useful indications if not 
reasonably accurate numerical results. Noteworthy is 
the fact that the relative motion of wind and water 
represents simply an extreme degree of stratified flow, 
moderately small-scale investigations of wind-driven 
waves having yielded useful indications of the forces 
involved [18]. 
Previous mention of turbulence has been restricted to 
that resulting from the surface resistance or form re- 
1. Consult ‘Experimental Analogies to Atmospheric Mo- 
tion” by D. Fultz, pp. 1235-1248. 
1253 
sistance of the flow boundary. The diffusion resulting 
from such turbulence is known as forced convection. 
Related in mechanism but distinct in origin is that type 
of turbulent mixing resulting from an unstable density- 
stratification of a fluid, the result being known as 
free convection. Typical of free convection is the pattern 
of mean flow and eddy motion produced by a boundary 
source of heat below an otherwise quiet fluid. The 
heated fluid becomes less dense than its surroundings 
and tends to rise, and at the same time inflow toward 
the rising column of eddies is induced through displace- 
ment and entrainment. Although other thermodynamic 
effects are involved in both the original heating and the 
subsequent mixing and cooling, except under extreme 
conditions these remain secondary to the effects of 
gravitational acceleration and turbulent diffusion. In 
other words, the essential aspects of the free convection 
could be reproduced in water by the introduction of 
heat or finely dispersed bubbles at a lower boundary 
or by the removal of heat or introduction of sediment 
at an upper boundary. In view of the complexities 
involved in giving proper consideration to an additional 
dimension and to the corresponding flow and fluid 
variables, it is therefore expedient as a first approxi- 
mation to disregard the thermodynamic effects in such 
investigations and reduce the problem to one of 
mechanical (7.e., dynamic) similarity alone. 
Up to the present, laboratory studies of this nature 
have been restricted to the analysis of free convection 
under generalized conditions. There is no obvious 
reason, however, why similar techniques could not be 
applied to specific prototype conditions of boundary 
configuration and wind orientation; under any cir- 
cumstances, existing data obtained at small scale should 
be applicable at least approximately to general proto- 
type conditions. Results now at hand apply to con- 
vection from a point source and from a line source in 
Hb 
L_ DIFFUSION 
ZONE 
\ 
\ 
\ 
POINT \ 
SOURCE ~\i/ Lane 
r OTT MOTTO c 
Fie. 2.—Definition sketch for free convection above a source 
of heat. 
i 
My 
stagnant fluid and from a line source in a uniform wind 
[16]. In each case the convection was attained in air by 
means of heat (either low gas flames or electric hot- 
plates), the measurements of temperature differentials 
being reduced to specific-weight differentials by the 
simple ideal-gas equation. With reference to the defini- 
