Civil Engineering Reference
In-Depth Information
may be interpreted as the average duration of a
u
,
v
or
w
wind gust. Although the
covariance coefficient in many practical cases may become negative at large values of
τ
it is a usual approximation to adopt
()
(
)
exp
/
T
nuvw
,,
ρτ
=
−
τ
where
=
(3.23)
n
T
is usually in the range between 5
In homogeneous terrain, at heights below 100 m,
and 20 s, while
T
and
T
are in the ranges 2 - 5 and 0 - 2 s.
Fig. 3.4
Auto covariance coefficient for the along-wind turbulence component
Adopting Taylor's hypothesis that turbulence convection in the main flow direction
takes place with the mean wind velocity (i.e. that flow disturbances travel with the aver-
age velocity
V
), then the average length scales of
u
,
v
and
w
in the
x
direction are
given by
∞
x
f
()
L
VT
=⋅
∫
V
d
nuvw
,,
=⋅
ρ
ττ
where
=
(3.24)
n
n
n
0
These turbulence length scales may be interpreted as the average eddy size of the
u
,
v
and
w
components in the direction of the main flow.
While auto covariance functions (or coefficients) represent the time domain properties
of the turbulence components, it is the spectral densities that describe their frequency
domain properties. In the literature many different expressions have been suggested to fit
data from a variety of full scale recordings. The following non-dimensional expression
proposed by Kaimal et. al. [10] is often encountered in the literature:
