Civil Engineering Reference
In-Depth Information
sxy
,
z
. The corresponding covariance coefficients are defined by
where
=
or
f
f
(
)
Cov
s
,
nuvw
sxyz
=
,,
,
Δ
τ
⎧
⎪
⎨
(
)
nn
ρ
Δ=
s
,
τ
(3.33)
nn
2
Δ=Δ
Δ Δ
,
σ
⎪
⎩
f
f
f
n
The covariance properties in the wind field are in general decaying with increasing sepa-
ration
Δ
s
and time lag
τ
. A typical decreasing curve at
τ =
0
is illustrated in Fig. 3.7.
Fig. 3.7
Spatial cross covariance properties of the wind field
0
The situation at
τ =
is particularly interesting because
∞
nuvw
sxyz
,,
,
=
⎧
⎪
⎨
s
(
)
(
)
L
∫
s
,
0
d
s
=
ρ
Δ
τ
=
Δ
(3.34)
n
nn
,
Δ=Δ
Δ Δ
⎪
⎩
f
f
f
0
is a characteristic length scale that may be interpreted as the average eddy size of com-
ponent
n
in the direction of
s
. For instance, the length scales
L L
and
x
f
L
are
quantities representing the average eddy size of the
u
,
v
and
w
components in the
direction of the main flow. They have previously been presented in Eq. 3.24, and since
they obviously can be extracted directly from two point data and Eq. 3.34, the use of
Taylor's hypothesis behind Eq. 3.24 is obsolete. The remaining six length scales
s
x
x
f
f
,
u
v
L
with
are the corresponding quantities that represent the spatial
properties in a plane perpendicular to the main flow direction. Typical decay curves for
the
u
component are shown in Fig. 3.8, illustrating the spatial interpretation of the inte-
gral length scales.
and
nuvw
=
,,
syz
=
,
f
f
