An acoustic Doppler velocimeter (ADV) for the ... - LTHE

1564 N. Gratiot et al. / Continental Shelf Research 20 (2000) 1551}1567
Fig. 9. Distribution of a velocity record (plotted in Fig. 8) measured in a mixing tank containing #uid mud.
A Gaussian distribution (*) is superimposed.
analysis, the missing values in the record were replaced with the last preceding
validated velocity datum. The propeller generated both a mean rotating #ow and
turbulence. For this record, the mean velocity in the direction of propagation of
ultrasonic waves is ;M "1.25 cm s and the rms turbulent velocity is u"2.15
cm s. The histogram of velocity variations for the record considered in Fig. 8. is
shown in Fig. 9. The distribution is Gaussian, as shown by the Gaussian curve
superimposed on the data. This is a "rst indication that the statistical properties of the
turbulence are captured in the velocity records measured by the ADV. As random
white noise also displays a Gaussian distribution of events, a time frequency spectral
analysis of velocity records was made in order to estimate the proportion of the signal
corresponding to turbulent #ow and that associated with noise. The power spectrum
of turbulent #uctuations is presented in Fig. 10. Energy density decays as frequency
increases. The threshold level reached at frequencies higher than 70 Hz indicates the
level of noise contained in the record. In hydrodynamic turbulent #ows, the energy
density decays for increasing frequency, a phenomenon that is associated with a transfer
of energy from low frequencies (large eddies) to high frequencies (small eddies). In
Fig. 10, the energy spectrum decay versus frequency follows approximately a power
law of the form E( f )+f , which is the decay law predicted by Kolmogorov's
theory for a homogeneous isotropic turbulent #ow. Although these observations do
not prove that the turbulence measurements are quantitatively accurate, they provide
consistent indications that ADV measurements capture the hydrodynamic properties
of turbulence and, in particular, that aliasing due to an insu$cient rate of data
validation is unlikely to occur.