Geoscience Reference
In-Depth Information
The effects of spatial averaging and sensor separation associated with turbulent
velocity measurements tend to be three-dimensional. As a result they tend to appear
as spectral transfer functions only in three-dimensional wavenumber space. In the
case of three-component sonic anemometers, for example, the spectral transfer
functions depend on three acoustic path vectors
L
i
and on three path-separation
vectors
d
i
. Thus, to determine the effects of path length and separation on one-
dimensional velocity spectra we must integrate the spectral transfer function over
two wavenumbers:
∞
∞
F
1m
T(
κ
,
L
1
,
L
2
,
L
3
,
d
1
,
d
2
,
d
3
)φ
ij
(
κ
)dκ
2
dκ
3
.
=
(16.79)
ij
−∞
−∞
This can make the interpretation of velocity measurements from three-dimensional
sensor arrays quite complicated at wavenumbers where the path averaging and
sensor-separation effects are significant (
Kaimal
et al
.
,
1968
).
Wyngaard
(
1968
,
1969
,
1971
) has calculated the spectral response of hot-wire
velocity and vorticity probes and resistance-wire temperature sensors;
Kaimal
et al
.
(
1968
) have done the same for three-component sonic anemometers; and
Gal-Chen
and Wyngaard
(
1982
) have extended the analysis to multiple-Doppler radars.
16.2.5 Measuring resolved and subfilter-scale variables
Tong
et al
.
(
1998
) developed a technique for measuring resolved and SGS variables
in the surface layer. Using high-resolution (256
3
) LES data, they first established
that filtering in the two horizontal directions is a good surrogate for three-
dimensional filtering. They then showed that filtering in time and using Taylor's
hypothesis can be an adequate substitute for filtering in the streamwise direction.
These simplifications allow the use of a single linear array of sensors oriented in
the cross-stream direction. A variable
f(x,y,t)
, say, at a given height
z
is filtered
in time by using a running average such as
N
1
f
t
(x,y,t)
f(x,y,t
=
−
nt).
(16.80)
2
N
+
1
n
=−
N
+
These filtered variables from2
N
1 (five, say) sensors spaced in the lateral direction
are then combined with equal weights to simulate lateral filtering:
2
y, t )
.
(16.81)
1
5
( f
t
)
y
f
t
(x, y
+
f
t
(x, y
+···+
f
t
(x, y
=
−
2
y, t )
−
y, t )
+
