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In-Depth Information
10 0
Φ∼
16.5 −
Γ∼
1
0.2
10 −1
0
10 −2
-0.2
10 −3
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Time (a.u.)
10 −4
12
13
14
15
16
17
Figure 15.11. Example of reconstruction of the instantaneous
frequency scattered by a moving sphere in a swirling flow of
water. The color image represents the spectrogram computed
with usual Fourier analysis time-frequency analysis (the width of
the frequency trace illustrates the incertitude due to Heisenberg
constrains) to which is superimposed the estimation given by
the AML method (solid black line). From Mordant [2001]. For
color detail, please see color plate section.
v z (m/s)
10 0
ϕ
Γ
ϕ
Γ
12.5
14.6
16.7
18.8
20.8
22.3
25
1
1
1
1
1
1
1
16.8
12.6
16.8
30
10 −1
12.4
47
16.4
50
19
52
21
41
16.8
65
1000
10 −2
16.7
2.7
13.5
6.34
0.05
15.3
4.67
16.7
4.58
18.5
5.9
10 −3
20.8
4.23
instance when two particles were simultaneously present
in the measurement volume.
22.8
4.0
10 −4
15.3.1.3. Example of Acoustical Particle Tracking.
Acoustical tracking has been used in different experi-
mental facilities, including von Kármán swirling flows,
turbulent jets, and wind tunnels to investigate both the
characteristics of the flow and the dynamics of material
particles transported by the flow. Figure 15.12 represents
the probability density functions of the velocity and accel-
eration of material particles transported in a turbulent
wind tunnel low. Velocity is found to have Gaussian statis-
tics while acceleration exhibits wide non-Gaussian tails,
even for particles much denser than the fluid.
10 −5
10 −7
-15
-10
-5
0
a z /< a 2 > (1/2)
5
10
15
Figure 15.12. Top: One-component Lagrangian velocity PDF
of finite-size part neutrally buoyant particles transported in a tur-
bulent wind tunnel flow. From Bourgoin et al. [2011]. Bottom:
Acceleration PDF of finite-size material particles with different
sizes and density (parameters and ) in the same wind tunnel
flow. From Qureshi et al. [2008].
15.3.2. Vorticity Measurements
instance to the interaction between vortices and the influ-
ence of global rotation as well as the turbulent cascade of
enstrophy at mesoscales for which the atmosphere and/or
the ocean can be considered as 2D.
Measuring vorticity has always been a challenge in
experimental luid mechanics, especially when small scales
are to be probed. We recall here that the vorticity of a
velocity ield
u ( = ∇×
u ). A
direct measurement of vorticity is usually done from spa-
tial derivatives of the velocity field. This is typically the
case with PIV or multiple hot-wire measurements. How-
ever, in either case, the spatial resolution is an issue when
flows are highly turbulent as neither PIV nor multiple
hot-wire probes are capable of resolving the smallest dis-
sipative scales of the velocity fields, which are essential for
an accurate estimation of a spatial derivative. We report in
this section an elegant measurement of the vorticity of a
flow based on the peculiar interaction between an acoustic
wave and the vortical structures of a flow. In the context
of atmospheric and oceanographic studies, this technique
may be particularly suited to address questions related for
u is given by the curl of
15.3.2.1. Principle. The method relies on the interac-
tion between an acoustic wave and the velocity gradients
in the flow. The scattering properties from this acoustic-
fluid interaction are non-trivial. Several theoretical and
numerical studies can be found on the subject [ Obukhov ,
1953; Kraichnan , 1953; Chu , 1958; Batchelor , 1957; Lund
and Rojas , 1989; Llewellyn Smith and Fort , 2001; Colonius
et al. , 1994]. In particular, using a Born approximation,
Lund and Rojas [1989] have shown that the scattered
amplitude of a plane acoustic wave by a turbulent flow
can be linearly related to the spatial Fourier transform
of the vorticity field of the flow. This property can be
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