1252 
Modern boundary-layer theory indicates that even 
the qualitative indications which Abe obtaimed cannot 
be considered trustworthy, since the separation pattern 
for a particular boundary configuration varies markedly 
with the usual Reynolds number [10, Vol. II]. In other 
words, as the quantity VL/» changes from a very small 
to a very large magnitude, at least four distinct types of 
flow may be recognized, as follows: (1) at extremely low 
values the viscous boundary layer extends a great dis- 
tance from the boundary, and the low-velocity flow near 
the boundary is quite stable; (2) at somewhat higher 
values the zone of viscous action decreases in thickness 
and stable eddies develop behind the major irregulari- 
ties; (3) at moderate values the boundary layer becomes 
thin but remains laminar, separation eddies forming 
more irregularly and passing off into the flow; (4) at 
high values the boundary layer becomes turbulent and 
the tendency toward eddy formation is restricted to the 
more angular portions of the boundary. The relative 
Reynolds-number ranges of these several types of flow 
depend to a considerable degree upon the form of the 
boundary configuration; no general values can therefore 
be given, but for rough indications reference may be 
made to standard diagrams of surface and form re- 
sistance for simple plates and bodies of revolution [15]. 
While the complete simulation of flow over gently 
undular terrain cannot be accomplished at model scale 
because of the extremely high velocities which would 
be required to maintain constancy of the Reynolds 
number, it so happens that flow past angular boundary 
configurations at all but very small scales and air 
speeds is essentially independent of viscous effects. 
In other words, at moderate to high Reynolds num- 
bers the separation pattern for such “‘unstreamlined”’ 
forms is determined almost solely by their geometry. 
Therefore, with geometric similarity of the boundary 
the normal air speed of a wind tunnel is sufficiently 
high for similitude to be obtained. Typical of such an 
investigation is the study at model scale of air currents 
in the vicinity of the Rock of Gibraltar [8], the labora- 
tory indications being in close agreement with observa- 
tions made at the actual site. 
If the terrain is not sufficiently irregular to ensure 
freedom from viscous effects, one is tempted to distort 
the vertical scale of the model until the necessary 
degree of angularity is secured. The success of such a 
procedure depends largely upon the degree of similitude 
to be obtained, since the theory of both the potential 
flow around a body and the viscous effects upon the 
basie pattern point to a gradual departure from simi- 
larity as the boundary geometry is distorted. It is 
altogether probable that the gain in freedom from 
viscous effects is wholly offset by the changes in pattern 
which this distortion produces. In other words, as the 
terrain in question becomes less irregular, true simili- 
tude can be approached in the model only by increasing 
the velocity of flew accordingly. The obvious limit of 
such increase is the onset of marked compressibility 
effects as the Mach number of the model approaches 
unity. 
In addition to the mean flow pattern and the pattern 
LABORATORY INVESTIGATIONS 
of the major eddies, which formed the basis of the 
Gibraltar study, the accompanying pattern of turbu- 
lence is often of importance. As in all turbulence studies, 
at least three characteristics of the turbulence may be 
involved: (1) the intensity, or root-mean-square ve- 
locity of fluctuation; (2) the scale, or mean eddy size; 
(3) the diffusivity, or eddy viscosity, which is pro- 
portional to the product of the tensity and the scale. 
For flow over relatively smcoth boundaries, the de- 
velopment of the turbulent boundary layer is primarily 
a function of the Reynolds number, and model simi- 
larity would hence require approximately the same 
magnitude of the Reynolds number as in the prototype. 
While this is practically out of the question, enough is 
now known about the mechanics of the boundary layer 
to permit evaluation of prototype conditions by analyti- 
cal rather than experimental means [5]. With uneven 
boundaries, however, particularly those which involve 
large-scale irregularities rather than small-scale rough- 
ness, not only is the boundary-layer theory incomplete 
but specific problems are more readily subject to model 
investigation. Fortunately, although true atmospheric 
turbulence contains eddies varying over an extremely 
wide range of intensity and scale, it is usually the 
larger magnitudes of each which are of major interest 
and are at the same time most nearly reproducible by 
models. 
Laboratory investigations of the turbulent diffusion 
of heat, gas, and water vapor in the neighborhood of 
smooth boundaries have frequently been made—but as 
general studies of the mechanics of such diffusion rather 
than as specific model studies of particular prototype 
conditions. In connection with the previously mentioned 
training film on chemical warfare, on the other hand, 
evaluation of diffusion characteristics for various rough- 
boundary configurations studied at the lowa Institute 
required the detailed measurement either of the turbu- 
lence characteristics or of the actual diffusion of some 
material introduced into the flow. Typical of such 
evaluation, for example, was the experimental deter- 
mination of the diffusion of gas or smoke from pomt 
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a 
4 ale uUeS OF cVLYQ~> 
OO}O 
4 0 
—— 
8 10 l2 14 16 
“4 = c 2 
xX/L 
Fig. ¢.—Generalized diffusion patterns at height Z for two 
different block arrangements. 
and line sources in typical urban districts. Owing to 
the pronounced angularity of the model buildings, the 
pattern of turbulence (or at least the large-scale portion 
