Civil Engineering Reference
In-Depth Information
Caution should be exercised as the variation in
n
c
values is considerable (see Solari &
Piccardo [6]). The simple expression in Eq. 3.41 has the obvious disadvantage that the
normalised co-spectrum becomes unity at all
f
=
, whereas a typical normal-
ised co-spectrum will decay at any value of
f
as illustrated in Fig.3.9. It also has the
disadvantage that it is positive in the entire range of
Δ
when
0
s
. (It may be shown that this is in
conflict with the definition of zero mean turbulence components.) Under the assumption
of isotropic conditions, Krenk [12] has derived the following expression applicable for
the along-wind
u
component
Δ
κΔ
⋅
s
⎛
⎞
ˆ
(
)
(
)
Co
s f
,
1
exp
s
Δ
=−
⋅
−⋅
κ
Δ
(3.43)
⎜
⎟
uu
2
⎝
⎠
12
2
⎡
⎤
2
⎛
⎞
2
π
f
1
1.34
⎛ ⎞
⎢
⎥
where
κ
=
+
⎜
⎟
⎜ ⎟
⎜
⎟
x
⎢
V
⎥
L
⎝ ⎠
⎝
⋅
⎠
u
⎣
⎦
Fig. 3.9
Typical reduced co-spectrum variation
