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

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7.3 Spatio-temporal correlations with ×_ñò¬\
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first order moments of the velocity fluctuations within this domain. It could be shown that
the structures of the spatio-temporal auto-correlation functions of the stream-wise (ªS·· ) and
span-wise (ªSÙ&Ù ) velocity fluctuations are quite similar (shape, size and temporal decay) when
the span-wise and wall-normal dependence is considered, whereas their cross-correlation ªS·Ù
is necessarily zero due to symmetry. Also, the characteristic shift of the largest correlation
value towards higher velocity regions with time agrees well. The wall-normal correlations, on
the other hand, are relatively small and their maximum decreases fast with increasing time. As
a consequence, the spatial extent of regions where most of the Reynolds stresses are produced
must be relatively limited. The correlation function of the stream-wise vorticity component
also reveals a short spatio-temporal correlation length and a displacement towards higher velocity
regions. Although a consistent interpretation of the presented results is conceivable, the
instantaneous velocity fields need to be analysed for further evidence.
y + ,∆t + )
R uu
(31+∆
1
0.8
0.6
0.4
20.4
21.9
27.3
31.1
34.6
39.9
43.3
R uu
(198+∆y + ,∆t + )
1
0.9
0.8
0.7
185.4
198.4
196.3
198.5
200.6
205.2
216.4
y + ,∆t + )
R uu
(52+∆
0.2
1
0.8
0.6
0.4
¨
0
50 ¨
100
¨
© 150 200
y + +∆y +
© 250
¨
300
34.1
41.6
48.5
52.6
56.6
63.6
77.1
R uu
(301+∆y + ,∆t + )
0.6
100
1
0.9
0.8
0.7
© 150
¨
200
© 250 300
y + +∆y +
© 350
¨
400
288.1
298.6
299.1
301.3
302.4
305.6
326.3
y + ,∆t + )
R uu
(101+∆
0.2
1
0.8
0.6
0.4
¨
0
50 ¨
100
¨
© 150 200
y + +∆y +
© 250
¨
300
90.4
99.4
98.8
101.2
104.4
111.2
132.3
R uu
(398+∆y + ,∆t + )
0.6
200
1
0.9
0.8
0.7
© 250
¨
300
© 350 400
y + +∆y +
© 450
¨
500
394.7
387.5
398.6
400.8
402.9
421.4
0.2
¨
0
50 ¨
100
¨
© 150 200
y + +∆y +
© 250
¨
300
0.6
300
© 350
¨
400
© 450 500
y + +∆y +
© 550
¨
600
FIGURE 7.14: Representation of the ˜ ·· correlation at ˜$ûšÀœ§§žž in the vicinity of the maximum
for various wall distances © » of the fixed point and temporal separation between the measurements
(ÉKøÓ» š Ð ž Æ ÏcÆ Ð§ÆØÆ ž Æ ÈÐ§Æ È7ÏcÆ ÈKÐ ž ).
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