turbulent velocity profile

Jun 2014
I cant understand that the( in the second picture) logarithmatic law velocity profile is quite accurate for y larger than 30 , but neither velocity profile is accurate in the buffer layer ,, 5 <y<30 . Can someone help to explain it ? How do the author know that it's not accurate for 5 <y<30 ? in the graph , i could only see the range is from (10^0) to (10^4) ,



Apr 2008
Bedford, England
One of the issues with computational fluid dynamics is that there is no full mathematical description of the boundary flows.
(To my knowledge) all boundary flow descriptions are experimentally derived.

Basically one looks at the problem and decides which parameters alter the result, perform lots of experiments with different values for these parameters, thin find a mathematical equation which provides a reasonable fit to the experimental data.

The trouble with any empirically derived relationship is that one cannot know that it works beyond the limits of the experiments against which it was originally derived.
Another problem with deriving boundary expressions is the physical difficulty of making accurate experimental measurements in the boundary layer very close to the wall.