Civil Engineering Reference
In-Depth Information
at low turbulence and high values of V can be approximated by
()
ut
1
⎡
⎤
()
2
qt
≈
ρ
V
12
+
⎦
(3.10)
⎢
⎥
u
2
V
⎣
2
it is seen that the mean value of
q
is
qq
V
2
while the fluctuating part is
==
ρ
uV
()
. The standard deviation of the velocity pressure is then
, where
ρ
Vu t
σ
=
ρ
V
σ
σ
q
u
u
u
is the standard deviation of the along wind turbulence component. Thus, an extreme
value of
q
may be obtained by
1
2
2
max
q
=
ρ
V
=
q
+
k
σ
(3.11)
u
u
p
q
u
max
where
k
is a peak factor (see chapter 2.4, Eq. 2.45). The following is then
p
obtained:
1
1
2
2
V
V
k
V
VV k
12
pu
V
(3.12)
ρ
=
ρ
+
ρ
σ
⇒
=
+
σ
max
p
u
max
2
2
3.2 Single Point Statistics of Wind Turbulence
While we in the previous chapter were dealing with long term statistics of ten minutes
mean values, i.e. performing statistics on a data base covering many years of observa-
tions of
V
, we shall now return to short term statistics on the fluctuating flow compo-
nents
()
()
()
wt
. It is single point recordings of these variables within a sta-
tionary period of
T
=10 min that provide the source for determination of their time and
frequency domain statistical properties. The sampling frequency within this period is in
the following assumed to be large, rendering a sufficiently large data base for the extrac-
tion of reliable results. As shown in chapter 1.3, at a certain point
ut
,
vt
and
(
)
, e.g. at
x yz
,,
f
z
10
or at a reference point relevant to the structure in question, it is assumed that
()
=
m
f
()
()
()
()
Ut
V ut
, and that the turbulence components
ut
,
vt
and
wt
are stationary
=+
and have zero mean values.
