ATMOSPHERIC TURBULENCE AND DIFFUSION 
the w, In z plots are no longer linear, but are convex to 
the a-axis in the lapse period and concave to the same 
axis in the inversion period. Deacon concludes that, in 
all conditions, 
di/dz = az* (¢ S$ 13 m) 
(a independent of z), with 8 > 1 for superadiabatic 
gradients, 8 = 1 for the adiabatic lapse rate and B < 1 
for inversions. Thus the logarithmic profile is valid only 
for adiabatic gradients, and for other conditions Deacon 
proposes the profile 
2+ tall)! 
where zo , as usual, is the roughness length. 
For many applications, and particularly those dealing 
with diffusion, the logarithmic profile makes the rele- 
vant differential equations difficult to handle, and in 
such problems a simple power law, @ = t%(z/2)?, is 
usually employed as an approximation. This is fairly 
satisfactory except near a rough surface, where a modi- 
fication has to be introduced to allow for the effect of the 
irregularities (v. Calder [7] and Sutton [65]). When a 
law of this type is adopted the effect of temperature 
gradient is shown by variations in the index p. Values 
of p ranging from 0.01 (large lapse rate) to 0.77 (large 
inversion) have been given (Brunt [4], Frost [20]), and 
it is generally accepted that the value p = 1 is 
appropriate for small gradients, except very near the 
ground or over very high vegetation. For conditions 
very near the ground (2 < 2 m), the evidence shows 
that the logarithmic profile can be assumed without 
serious error for all except the largest gradients by 
allowing the roughness length and the Ka4rm4n constant 
to vary with temperature gradient, but if deeper layers 
are involved, the departure of the velocity profile from 
the logarithmic form must be taken into account. 
The profile of mean velocity near the surface has 
now been thoroughly explored, but the same cannot be 
said about the eddy velocities. One of the great diffi- 
culties in dealing with atmospheric turbulence com- 
pared with that found in wind tunnels is that the 
natural wind is made up of fluctuations of widely 
different periods, and the interval of measurement and 
the response characteristics of the anemometer must 
always be taken into account, particularly in problems 
of diffusion. The most reliable data on the velocity 
fluctuations relate to what Scrase [59] has called ‘‘inter- 
mediate-scale turbulence,” mean values over intervals 
of the order of a few minutes. It was early demonstrated 
by Taylor and later confirmed by Scrase [59] and 
Best [2] that such turbulence is anisotropic near the 
ground, with the cross-wind component about 50 per 
cent greater than either the downwind or vertical com- 
ponent at about 2 m over downland in conditions of 
small lapse rate. Best [2] has given a reasonably com- 
plete picture of the behaviour of the three components 
near the ground by making use of the bi-directional 
vane, and he concludes that the anisotropy is likely to 
be negligible at heights greater than about 25 m. 
As would be expected, the eddy velocities obey the 
(2 = a), 
499 
Maxwell law of frequency distribution, and Best has 
given the precise formula. Best also examined the 
variation of the fluctuations with height and found that 
both the lateral and vertical components increase slowly 
from 25 cm to 5 m and presumably begin to decrease at 
higher levels. For winds blowing over the sea there is 
still less information, but all three components of gusti- 
ness are much reduced compared with those over land, 
probably to about one half. 
At the present time, much remains to be learnt 
concerning the structure of turbulence near the ground. 
While it is known that the amplitude of the oscillations 
shows a continuous decrease as the temperature gradient 
changes from lapse to inversion, it is impossible to 
quote reliable laws, even empirical, which express this 
fact quantitatively. There is very little information on 
the distribution of energy among the fluctuations; 
Brunt [4] has deduced from the work of Scrase that 
near the ground and in conditions of small lapse rate 
most of the eddying energy is associated with oscilla- 
tions of periods less than five seconds, but a complete 
picture of the eddy spectrum is not yet available. 
The Humidity Field. Investigations into the propaga- 
tion of high-frequency electromagnetic waves over the 
surface of the earth have directed attention to the 
study of water-vapour gradient in the atmosphere, and 
fairly detailed accounts have been given by Sheppard 
[60] and Burrows and Attwood [5]. In the daytime, 
vapour pressure in the lower layers decreases with 
height even over ground which appears dry, but during 
the inversion period the gradient may change sign 
(vapour pressure increasing with height), often with 
the formation of dew. Sheppard concludes that in the 
main the vapour-pressure profile conforms fairly closely 
to a logarithmic law up to 100 m at least, and that 
there is no marked diurnal variation. Information con- 
cerning the distribution of water vapour over the sea 
is to be found in the papers by Craig, Emmons and 
Sverdrup cited above. 
The Transference of Momentum, Heat and Water- 
Vapour in the Vertical. In Reynolds theory the transport 
of momentum by turbulence across a horizontal plane 
is expressed by the eddy shearing stress r = —pu’w’, 
if the molecular term is disregarded. In the surface 
layers, it is customary to assume that 7 is virtually 
independent of height and therefore equal to its value 
at the surface, to. The frictional effect of the ground 
may also be expressed by means of the skin-friction 
coefficient Cp by writing 
where &% is the mean velocity at some fixed height. 
Laboratory investigations show that the skin-friction 
coefficient of a fully rough surface is virtually inde- 
pendent of the viscosity of the fluid, and in these 
small-scale experiments Cp usually varies between 10~% 
and 10~°. Taylor [75], by measuring the approach to 
the gradient wind in the friction layer from pilot- 
balloon observations, found Cp for downland to be 
about 5 X 10-%, and very similar values were found 
hy Sutcliffe [62], using a somewhat different method. 
