Geoscience Reference
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This relationship ( 4.15 ) was derived from the data taken at altitudes 50 to 100 m
above ground level. Numerous data taken in the surface layer give slightly smaller
value of the coefficient: 0.62-0.7 (see e.g. Stull 1988 ). Using this relationship one
can estimate the vertical structure of momentum flux in neutrally stratified ABL
by means of a SODAR (or any other remote-sensing tool) that is able to measure
σ
2
w accurately enough (Kouznetsov et al. 2007 ). Figure 4.29 shows empirical data
which give the dependence of the proportionality factor in ( 4.15 ) as function of
the flux Richardson number, R f . Mandatory input for the determination of the flux
Richardson number, i.e. the heat flux, cannot be observed from SODAR measure-
ments, but must be specified from separate surface heat flux measurements and the
assumption that the heat flux decreases linearly to zero at the top of the mixing layer
(Kouznetsov et al. 2007 ).
Basically the same idea, on which ( 4.15 ) is founded, can be employed to estimate
vertical profiles of the turbulent viscosity,
ν t or eddy viscosity of the air (Emeis
2004 ; Kouznetsov et al. 2007 ). This turbulent viscosity is an important parame-
ter in turbulence parameterization schemes for meso-scale numerical flow models.
Frequently, this turbulent viscosity is termed turbulent vertical exchange coefficient,
K m,v . It is defined as
u w
K m , v = ν t =−
,
(4.16)
u
z
As the vertical turbulent momentum flow is much larger than the mean vertical
momentum flow, this is the most important component that has to be parameterized
in the numerical simulation of turbulent boundary laye r flow. Applyin g ( 4.16 )toa
homogeneous Prandtl-layer (i.e. putting u
2
u w and u
u
κ
for
/
z for
z , with the
von Kármán constant
0.4) leads to the well-known expression for the turbu-
lent exchange coefficient K m,v (
κ =
= ν t ) that increases linearly with height if the wind
speeds increases logarithmically with height:
ν t =
u
κ
z ,
(4.17)
Fig. 4.29 Factor of
proportionality between the
turbulent vertical momentum
flux and the square of the
standard deviation of the
vertical wind component as
function of atmospheric
stability expressed in terms of
the flux Richardson number,
R f . From Kouznetsov et al.
( 2007 )
 
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