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

5 Investigation of the xy-plane
of conservation equations for the Reynolds stresses [37, 89]. Of primary interest are ÎV¼ÐÏ'Ñ the
ÎмÐÑÏ and correlations and their dependence on the wall distance, because these functions are
mainly responsible for the turbulent mixing in wall-bounded flows according to the Reynolds
equation in the boundary layer approximation on page 70. For the interpretation it is important
to keep in mind that the first subscript indicates the velocity component at the fixed point
while the second one indicates the component which is spatially shifted for the calculation
of the cross-correlation. There are two surprising results, namely the different height of the
correlation in the vicinity of the wall and the shift of the maximum towards the wall (when
the stream-wise velocity component is fixed) or away from the solid boundary (when the wallnormal
velocity component is fixed). This result will be further examined in chapter 6.
5.4 Properties of coherent velocity structures
The multi-point correlations presented in the previous section furnish information about the
average size, shape and coherence of the flow structures being present in the flow field, and
they provide valuable details required for the interpretation of near-wall turbulence in terms
of Reynolds equation and multi-point correlation equations. However, as the flow structures
have a history of development while they are transported downstream, the spatial correlation
functions include realizations of a large number of structures at various stages of their life
history. As the details about the individual flow structures are averaged out by the statistical
approach, the organisation of the individual coherent flow structures, their significance for the
production of turbulence and their relation with respect to proposed vortex models will be
investigated in the following. Unfortunately, this is not a trivial task because the selection of
typical structures is subjective as the outcome of such an approach is always strongly coupled
with the specified criteria. In other words, it is always possible to find structures which nicely
match with the models proposed in the first chapter or structures with other desired properties.
In order to minimise this well known problem, several techniques have been successfully
exploited in the past, such as the variable interval time averaging (VITA) method, which
compares the short term variance of a flow variable with respect to a chosen threshold level,
or the variable interval space averaging (VISA) method, which allows to detect structures
with similar spatial structure. However, these methods, which were mainly developed for the
analysis of time-resolved hot-wire measurements, are not well suited for the analysis of PIV
velocity fields. Therefore flow structures will be investigated here which appear frequently and
with sufficient strength in the essential Reynolds stress component. The first criterion selects
structures which are dominant with regard to their occurrence and the second one identifies
structures which are dominant in terms of turbulent mixing and production of turbulence.
5.4.1 Shear-layer
The basic coherent flow structure that can be easily observed in the áEÄ -plane of a turbulent
boundary layer (stream-wise wall-normal) is the so called shear-layer. When moving with
the appropriate convection velocity, or after subtracting the local mean velocity, this structure
appears as a slightly-inclined low-speed region, often several thousand wall-units in length
and some 100 wall-units in height (their width is largely unknown). The inclination angle of
the shear-layers relative to the wall was the subject of several studies [9, 28, 50, 62, 80]. The
general consensus is that this angle depends on the distance from the wall, as indicated by the
90