ATMOSPHERIC TURBULENCE AND DIFFUSION 
By O. G. SUTTON 
Military College of Science, Shrivenham, England 
THE AERODYNAMICAL BACKGROUND 
The Nature of Turbulent Flow. A particle im a stream 
of fluid ean never follow a perfectly smooth path 
because of minute random disturbances arising from 
the molecular structure of the fluid (Brownian motion), 
but observation shows that, in certain circumstances, 
oscillations appear in the path which are much too large 
to be ascribed to molecular agitation. Such irregular- 
ities must imply the existence of rapid and apparently 
random fluctuations in the velocity of the stream, con- 
stituting a permanent and characteristic feature of this 
type of flow. Turbulence can hardly be defined in a 
strict mathematical sense, but is generally understood 
to imply a motion characterized by a continuous suc- 
cession of such finite disturbances and in this sense 
nearly all natural motion, whether of water or of air, 
is turbulent. Only exceptionally is there found in nature 
a truly nonturbulent or laminar flow, in which the 
only random disturbances are the infinitesimal fluctua- 
tions due to molecular agitation. 
Anemometer records show that in general, and especi- 
ally in the lower layers of the atmosphere, the wind is 
highly turbulent, the velocity being a complex of oscilla- 
tions of duration varying from a fraction of a second 
to many minutes and of an amplitude which is often 
a substantial fraction of the average speed. Similar 
irregular oscillations are shown by direction indicators, 
so that the speed of the wind changes not only from 
instant to instant but also from point to point of space. 
A complete specification of the velocity field over even 
a limited portion of the atmosphere is in practice unat- 
tainable and, to make progress, attention must be 
concentrated upon mean values and other statistical 
functions of the velocity. The study of atmospheric 
turbulence is chiefly concerned with the analysis of the 
mean distribution of momentum, heat and suspended 
matter in, and as a result of, this highly complex and 
rapidly changing field. 
Air flow near the surface of the earth, the region in 
which atmospheric turbulence is of greatest importance, 
resembles in many respects turbulent motion in long 
straight pipes or near solid boundaries, as in wind 
tunnels, and aerodynamics thus affords a natural and 
convenient starting point for the meteorological prob- 
lem. The earliest recognition of two distinct types of 
flow—laminar and turbulent—seems to have been made 
by Hagen about 1839, but the detailed and systematic 
study of turbulence undoubtedly opens in 1883 with 
the famous experiments of Osborne Reynolds [49] on 
the flow of water through long straight glass tubes. 
Reynolds, by the simple device of making the flow 
visible by a thin stream of dye, was able to demonstrate 
that the transition from an orderly rectilinear motion 
(laminar flow) in which the thread of dye remains intact 
from inlet to outlet, to a disorderly or turbulent flow, 
evinced by the rapid disintegration of the filament of 
dye, takes place when the Reynolds number tid/y (@ = 
mean speed, d = tube diameter, » = kinematic viscos- 
ity) exceeds a certain value. At the same time other 
properties of the flow are changed, in particular the 
distribution of mean velocity across the pipe. In the 
laminar state the velocity profile is parabolic from the 
wall to the centre, but in turbulent flow the velocity is 
almost uniform over a central core, declining sharply to 
zero in a very thin layer adjacent to the wall itself. 
Such a change is easily accounted for in general terms. 
In laminar flow the only intermingling of adjacent 
layers of fluid is that due to molecular agitation (viscos- 
ity, conduction, diffusion), but in turbulent motion the 
fluid elements, because they follow extremely tortuous 
paths, transfer momentum, heat and matter freely 
from one layer to another and thus tend to smooth out 
local differences in velocity, temperature and concentra- 
tion of suspended matter. In other words, the principal 
effect of the turbulence is to cause enhanced mixing, 
and it is this aspect which is of paramount importance 
in meteorology. Very similar features are found in flow 
near solid surfaces. When a uniform stream of air meets 
a solid body, the influence of viscosity is felt only in 
the immediate vicinity of the surface, in the so-called 
boundary layer, a very shallow region characterized by 
large velocity gradients. Flow in such layers may be 
laminar, partly laminar and partly turbulent, or wholly 
turbulent. In a laminar boundary layer the velocity 
increases fairly regularly from the wall to the free 
stream, but in a turbulent boundary layer the velocity 
profile is much more uniform over the greater part of 
the layer, decreasing sharply to zero on approaching the 
wall itself. The effect of the turbulence is to bring down 
elements of fast-moving air from the free stream to the 
wall and, conversely, to remove the retarded air at the 
wall into the free stream so that, except im the immedi- 
ate vicinity of the surface, the velocity gradient is 
much reduced compared with that found in laminar 
flow. 
These observations have their counterparts in natural 
flow near the ground, but here the problem is much 
complicated by two extremely important differences. 
Laboratory investigations at low speeds deal almost 
exclusively with fluids in which marked density differ- 
ences do not exist and for which the effects of gravity on 
the flow are negligible. The maintenance of the turbu- 
lent state calls for a continuous supply of energy to be 
used in moving elements of the fluid from one level to 
another. If the lower layers of the fluid considerably 
exceed in density those above, the work which has to be 
done against the gravitational field in lifting masses of 
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