The significance of coherent flow structures for the turbulent mixing ...

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7 Investigation of the yz-plane
The interpretation of the results presented in figure 6.30 on page 133 was based on the assumption
that the spatial variation of the instantaneous turbulent velocity signal § ¹ Î Á ­ ¼ can be
transformed into a time dependent velocity signal § ¹|­ Á:(¼ at a fixed point according to
(7.1)
It is obvious that this so called Taylor hypothesis is certainly valid when the local convection
¦ velocity is large relative to the turbulent § fluctuations . However, the statistical results
shown in figure 5.3 on page 77 indicate that the maximum of the non-dimensional streamwise
velocity fluctuation is around 3 at ­ ® Ê ª Ç
and the average velocity is roughly 10 at
the same wall location according to figure 5.2. Although the ratio between both values is
only 0.3 at the measurement location where figure 6.30 was recorded, further evidence is required
to justify the assumption made because it is not evident ¦ that is the correct convection
velocity of the flow structures. For this reason the dependency of the spatio-temporal correlations
of the velocity fluctuations will be investigated in this chapter. In addition, various
spatial correlation and cross-correlation functions of the velocity fluctuations will be investigated
to validate the concepts proposed in chapter 6 to explain the turbulent mixing by means
of coherent structures. Furthermore the dimensions of the shear-layers in the ­ Ï -plane will
be considered and the characteristic features of the stream-wise vortices will be examined as
well as their significance for the turbulent mixing. This is of great interest as pointed out in
the introduction, because it is generally assumed that these vortices play a dominant role for
the momentum exchange in wall bounded flows, as indicated in figure 1.3. This work can
be seen as a completion of the conventional PIV investigation described in [13] and the flow
visualisation described in [28]. Here only the main results will be analysed in detail. The additional
information presented in the following may serve for comparison with the predictions
of fundamental turbulence models and for the validation of numerical flow simulations in the
future.
7.1 Experimental set-up
The multiplane stereo PIV technique in the configuration utilised for this investigation consists
of four pulsed Nd:YAG lasers (BMI) each with an output energy of 255 mJ per pulse at ¢ ¿
532
nm, two optical benches for the generation of independent light-sheets (one for each state
of polarisation), and four Peltier cooled high resolution cameras (PCO) with 1280 by 1024
pixel resolution and 12 Bit dynamic range. The schematic arrangement of the equipment
with respect to the test-section is outlined in figure 7.1. This arrangement follows directly
from the experimental setup, described in section 6.1, after rotating the orientation of the
135