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

6.2 Statistical properties of the buffer layer
stream-wise and wall-normal direction with sufficient strength (lower curve of figure 6.8) as
the total length of the low-speed structures are several thousand wall-units in length according
to the size of the Ã Ñ˜Ñ correlation, shown in figure 6.5. This is fully consistent with the size of
the ÃËÌË correlation and the results in [44]. The span-wise extent of the flow-structures associated
with the production of turbulence can be estimated best from the upper right graphs of
figure 6.9 and the phase relation between both orthogonal fluctuations from the location of the
maximum shown in the upper left graphs of the same figure. Apart from the structural details
of the flow regions associated with the turbulent exchange in wall-normal and stream-wise
direction, it is important to consider the cross-correlation with the span-wise velocity fluctuations
because any outflow of fluid induces an organised span-wise flow motion towards the
lifting structure due to continuity. In addition, as in isotropic turbulence this quantity must be
zero, these correlations indicate any departure from this ideal situation which is mathemati-
+ +
R uw(y =30)
R (y =30)
vw
∆ z +
∆ z +
∆ z
+
+
R uw(y =20)
+
R uw(y =10)
+
R vw(y =20)
+
R vw(y =10)
∆x + ∆x +
FIGURE 6.10: Two-dimensional spatial cross-correlation function of fluctuating stream-wise with
span-wise velocity components ÐÒÑ (left) and correlation of wall-normal with span-wise components
Ð Ë (right) measured at Ó ®xÔz֥آÙÛÚ¥Ø
and Ü Ø
(top to bottom).
111