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

6.2.3 Spatial cross-correlation functions
6.2 Statistical properties of the buffer layer
For phenomena associated with the production of turbulence the cross correlation ÃË Ñ is more
important than the primary components of the correlation tensor, as ÃË Ñ reflects the size and
shape of the structures being responsible for the transport of relatively low-momentum fluid
outwards into higher speed regions and for the movement of high-momentum fluid toward
the wall and into lower speed regions. This correlation was first studied by Tritton in 1967
by using a pair of hot-wire probes 2.1 m behind a trip-wire at free-stream velocities between
Þ¥¤ È Ç
m/s and È ¤ ª m/s [100]. The boundary layer thickness was Þ À mm and the Reynolds number
Âħ¦ ¿©¨¨ ÀÀ¢À . Due to technical reasons his results were only measured along the three
principal axes and at larger wall-locations, so that a direct comparison with the work presented
here is questionable. In the following, it is important to keep in mind that the cross-correlation
+
R vu (y =30)
+
R (-v)(+u) (y =30)
∆ z +
∆ z +
∆ z
+
+
R vu (y =20)
+
R vu (y =10)
+
R (-v)(+u) (y =20)
+
R (-v)(+u) (y =10)
∆x + ∆x +
FIGURE 6.8: Two-dimensional spatial cross-correlation function of fluctuating stream-wise with wallnormal
velocity components Ð Ë Ñ (left) and conditional cross-correlation of negative wall-normal with
positive stream-wise velocity Ð êJî Ë í ê ® Ñí (right) measured at Ó ® Ô×֥آÙÛÚ¥Ø
and Ü Ø
(top to bottom).
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