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

—
¯
6.2 Statistical properties of the buffer layer
calculate the absolute flow angles. The angles become comparable with the literature when
the stream-wise velocity fluctuation § is applied for the normalisation. This will be shown
later. Due to the strong dynamic of the velocity fluctuations in the buffer layer it is not evident
if the convection term in the conservation equations is large relative to the sum of the
production, diffusion and dissipation term, as required for the observation of coherent structures.
However, as the statistical results examined in this section indicate a strong relation
between various velocity fluctuations, it seems likely that the results are related with the motion
of organised or coherent flow structures. These structures, whose existence was already
assumed by Prandtl in 1925 for the derivation of the mixing-length theory, can be defined as
flow regions over which the simultaneous velocity fluctuations are correlated.
¯
°²±³´µ
­.®
°±³´µ
¦ ·.¸
mean rms
10 0.38 2.57
20 0.23 3.36
30 0.30 3.75
·.¸¹ ¦»º ¦~¼
10 1.00 2.86
20 1.43 3.76
30 1.59 4.20
·.¸¹ ¦»½ ¦~¼
10 -0.36 1.90
20 -0.90 2.43
30 -0.87 2.79
¾‚¸ ¦
10 0.17 9.32
20 0.14 6.84
30 0.13 6.42
TABLE 6.3: Statistical properties of the
absolute flow angles between the instantaneous
velocity components with respect
to the stream-wise direction measured
at • ® ’ 10, 20, 30.
6.2.2 Spatial auto-correlation functions
In order to link the statistical results of the previous section with the concept of coherent flow
structures, outlined in chapter 1 and section 5.4, the properties of normalised spatial correlation
and cross-correlation functions will be considered in this section, for theoretical details
see [53]. First of all, the average dimensions of the dominant flow structures will be deduced
from the primary components of the double correlation tensor measured in stream-wise spanwise
planes, at ®