x
I. K;hMPb D E FERN3
hccaiiw. rhc ground bunp assimilated to a tlat platc. one has
. .
. . . ..
- .
p f ' \ v ' - 0,
p ' w ' = 0,
p w , ~ = 0 for z = 0
Thus the horizontd strcss on the ground rcduccs to the viscous stress:
to = P V ... . I : . 0
1:
1 1 1 this sublayer neglecting the Reynolds stress the mean velocity profile is
giveri hy
U = (To/{)U)Z
Rut o u t of this sublayer the Reynolds stress becomes much larger than the
viscous stress. which can be neglected,
-To = -pU'W'
l h e essential step is made when one introduces [using one idea first
expressed by Boussinesq in 1872 (see Boussinesq, 1877)] the turbulent viscosity coefficient y*(:) defined by
(4.4)
y*(z) dii,/dz = - u'w'
whence
(4.5)
t o = p y * ( ~ )
dii/dz
Thc turbulent viscosity coefficient ~ * ( z )
[often designated by the symbol K,
the Austauschgriisse for Schmidt (1925)J had a leading role in the research
about turbulent atmospheric diffusion during the period 1920-1945.
Equation ( 5 ) shows clearly that there is a connection between the mean
velocity profile 1((z) and the turbulent viscosity coefficient y*(z).
To the degree of approximation assumed here, the density p being
constant. one can take advantage of the mean velocity profiles corresponding to turbulent flows of an incompressible fluid over a flat plate.
Around 1925 a power law was first proposed:
q z ) = Ii(q)(z/z,)P
Giblett (1932), using the measurements made at Cardington found for the
exponent p:
p = 0.01
if p > Po
p = 0.60 for large temperature inversions / 3 c 0
Rut in 1930 the logarithmic law was discovered for the mean velocity profile,
a law which was tested in the laboratory in many experiments and agreed