Reynolds Equation and Mixing Length Model Turbulent Flow Between Two Parallel Plates
Kolmogorov Scale
In the inertial sublayer
and
. The turbulent production then is given as
|
(35)
|
Experiment shows that in the inertial sublayer, production is equal to dissipation:
|
(36)
|
Kolmogorov scale is given by
|
(37)
|
Let
|
(37)
|
then
,
.
|
(38)
|
The turbulent macroscale near the wall is given as
|
(39)
|
or
|
(40)
|
Table of variation of the scales near a wall
![](formulas_2_phenom/image399.gif)
|
![](formulas_2_phenom/image401.gif)
|
![](formulas_2_phenom/image403.gif)
|
5 |
1.2 |
2 |
12 |
1.5 |
4 |
40 |
2 |
16 |
200 |
3 |
80 |
1000 |
4.5 |
400 |
Schematic variations of the macroscale and Kolmogorov scale in turbulent near wall flows |
From the table and the schematics diagram, it is observed that for , and a turbulent flow cannot exist. |