Geoscience Reference
In-Depth Information
Figure 7.23 Velocity spectra exhibiting the Kolmogorov interval are shown as solid lines. Straight
line indicates the
k
−
5
/
3
slope. Figure is reproduced from
Babanin & Haus
(
2009
) © American
Meteorological Society. Reprinted with permission
Kolomogorov interval are shown. The spectra were obtained as a Fourier transform of
the velocity
u
space series across the 30mm layer, with averaging over four wavenumbers.
Because the size of the image is less than the wavelength, the monochromatic-orbital-
motion peak cannot be seen in the spectrum. The spectra show a clear Kolmogorov subin-
terval at wavenumbers
k
m as should be expected for small turbulence scales
far away (in the Fourier space) from the energy source. The Kolmogorov-interval slope is
indicated with the straight line.
As was explained in
Section 5.3.4
, the level of the Kolmogorov interval contains infor-
mation about the volumetric kinetic energy dissipation rate
>
800 rad
/
dis
(e.g.
Veron & Melville
,
1999
). Since the wavenumber, rather than frequency spectra were measured with the PIV
system, the connection is simpler than
(5.66)
and does not have to rely on the rms advection
hypothesis of
Lumley & Terray
(
1983
):
8
2
/
3
18
55
dis
9
3
k
−
P
(
k
)
=
.
(7.75)
α
Using
(7.75)
to define
dis
, a dependence on the wave amplitude
a
0
was observed
(
Figure 7.24
). Given the large confidence intervals of the individual estimates and the
highly-intermittent behaviour of the observed turbulence, the experiment was repeated in
order to verify the consistency of the result. Data points denoted with circles were obtained,
for the same experimental setup, a year later than the asterisk data points.
Search WWH ::
Custom Search