Civil Engineering Reference
In-Depth Information
(
)
ˆ
ˆ
2
4
f
⋅
1
+
755.2
⋅
f
{}
fS f
⋅
n
n
n
,
nvw
,
(3.27)
=
=
2
(
)
11 / 6
σ
ˆ
2
1283.2
+
⋅
f
n
n
have the advantage that they contain only the length scales
x
f
L
that require fitting to
the relevant data.
3.3 The spatial properties of wind turbulence
The spatial properties of wind turbulence are obtained from simultaneous two point
recordings of the
u
,
v
and
w
components. It is taken for granted that the flow is ho-
mogeneous in space as well as stationary in time. Defining two vectors
()
()
()
(
)
ust
vst
wst
,
,
,
us
st
,
,
,
⎡
⎤
⎡
+Δ
+
τ
τ
τ
⎤
⎢
⎥
⎢
⎥
(
)
vs
st
υ
=
⎢
and
υ
=
+ Δ
+
(3.28)
⎥
⎢
⎥
a
b
⎢
⎥
⎢
(
)
⎥
ws
st
+Δ
+
⎣
⎦
⎣
⎦
where
sxy
,
or
z
,
τ
is a time lag that theoretically can take any value within
=
f
f
±
and
Δ
is an arbitrary separation (between the two recordings) in the
x
,
y
or
z
directions. Thus, the following three by three covariance matrix may be defined
Cov
Cov
Cov
⎡
⎤
uu
uv
uw
T
1
(
)
⎢
⎥
(
)
T
T
⎡
⎤
∫
Cov
Δ=
s
,
τ
Cov
Cov
Cov
=
E
υυ
⋅
=
υυ
(3.29)
⋅
dt
⎢
vu
vv
vw
⎥ ⎣
a
b
⎦
a
b
T
⎢
Cov
Cov
Cov
⎥
0
⎣
⎦
wu
wv
ww
where all the relevant covariance functions
mn uvw
sxyz
,
=
, ,
,
⎧
⎪
⎨
(
)
Cov
s
τ
,
(3.30)
Δ
mn
Δ=Δ
Δ Δ
,
⎪
⎩
f
f
f
sxy
,
z
.
may contain separation in an arbitrary direction
=
or
f
f
