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

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8 Summary
bulence, ª ù ·· ú ù ··yú namely ª ù ÔÔ ú ù ÔÔ:ú , ªIHJH , SªS·Ô , ûªSÔ· , ª ù ·Ô:ú ù ·$Ô ú , ª ù ··Ô ú ù ··Ô:ú , ª ù ·$ÔÔ ú ù ·ÔÔ ú , and
ù ÔÙ¥Ùú ù ÔËÙ&Ùú shows that the width of the correlations at a particular value decreases in general
ª
ù ·· ú ù ·· ú ª ù ··$Ô ú ù ··Ô ú , see page 88 and
ª
with increasing complexity of the ªS··
correlations
89. This implies a decreasing importance of the higher order correlations and establishes the
simplifications usually applied in the formulation of conservation equations for the Reynolds
stresses.
Chapter 6 illuminates the properties of the turbulent flow ª«§K%5®c¯ c at in stream-wise
span-wise (ñ Ã planes -planes) located ¹&»L% ¥Ö>c ¥ÖØÂ at . This region is of primary interest
according to chapter 5 because of the strong dynamic of the flow structures and the large
production of turbulence. In order to obtain information about the structural features of the coherent
structures, the size, shape and intensity of various spatial correlation, cross-correlation
and conditional-correlation functions are examined in detail, see page 106 to 113. It is shown
that the range of scales and span-wise periodicity of the coherent structures present in the flow
depends strongly on the wall-distance. The mean streak-spacing is 92 wall-units ¹¥»M% at
when estimated from the conditional correlation, see page 108, and the span-wise size of the
stream-wise vortices associated with sweeps measures 27 to 53 wall units ¹ » % ¥Ö>c ¥ÖØÂ
at
while those associated with ejection are 35 to 42 wall units in size for the same wall locations,
see page 107. However, the stream-wise size of these vortices is short relative to the length
of the low-speed streaks, and it seems that these vortices are induced locally by the lift-up
of low-speed streaks. This means that the stream-wise vortices which flank the low speed
streaks are no primary vortices. They are produced when the streaks move away from the
wall. The dynamics of the dominant structures is investigated by means of spatio-temporal
correlation, cross-correlation and conditional correlations functions measured in spatially separated
planes, see page 115 to 120. The conditional correlations yield information about the
space-time structure of the bursting phenomenon and allows to estimate the mean convection
velocity of the coherent velocity structures present in the near wall region. The analysis of
instantaneous velocity fields along with the probability density function of the Reynolds stress
äŸã component on page 121 implies, that most of the production of turbulence is associated
with low-speed streaks, but the magnitude of the instantaneous Reynolds stress äŸã
component
associated with streaks is relatively small, see page 123 and 124. The flow structures associated
with large values Ý äŸã¾Ý of on the other hand are frequently hair-pin like, see page 125 to
131. However, as the likelihood of these structures is quite small relative to the lifting streaks,
they do not contribute to the total Reynolds stress to a large extend in the near wall region.
The occurrence, intensity and main flow direction of the coherent structures is deduced from
the analysis of the joint probability density function of the velocity fluctuations, see page 101
to 104. It is shown that the largest flow (N
¡u¿
PO angles ) in wall-normal direction are usually
associated with ejection and sweeps, see page 105. In order to identify the structures responsible
for the characteristic velocity pattern observed in hot-wire investigations, the velocity
structure of the PIV measurements were analysed in stream-wise direction for various spanwise
locations, see page 132 and 133. It was shown that the characteristic velocity pattern
identified with the single point probes is caused by low-speed streaks. This could be further
confirmed by comparing significant parameters with the results reported in the literature.
Chapter 7 reveals the results measured in the wall-normal span-wise plane (¹¥Ã -plane) at
ª«§/%`®c¯ c and 15000. Of primary interest was the spatio-temporal dependence of the various
correlation functions and the validity of Taylor’s hypothesis because the interpretation of
the results presented in chapter 6 was partially based on the assumption that the flow struc-
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