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Unformatted text preview: called the logarithmic-overlap layer.
Thus by dimensional reasoning and physical insight we infer that a plot of u versus
ln y in a turbulent-shear layer will show a curved wall region, a curved outer region,
and a straight-line logarithmic overlap. Figure 6.9 shows that this is exactly the case.
The four outer-law profiles shown all merge smoothly with the logarithmic-overlap law
but have different magnitudes because they vary in external pressure gradient. The wall
law is unique and follows the linear viscous relation
u* yu* y (6.22) from the wall to about y
5, thereafter curving over to merge with the logarithmic
law at about y
Believe it or not, Fig. 6.9, which is nothing more than a shrewd correlation of velocity profiles, is the basis for most existing “theory of turbulent-shear flows. Notice
that we have not solved any equations at all but have merely expressed the streamwise
velocity in a neat form.
There is serendipity in Fig. 6.9: The logarithmic law (6.21), instead of just being a
short overlapping link, actually approximates nearly the entire velocity profi...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
- Spring '08