The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

CHAPTER 3. CHANNEL FLOW 43
Figure 3.6 shows the resulting profile for 〈v 2 〉 + plotted against DNS results.
3.4.6 Near-Wall Behaviour
Various researchers have analysed the limiting behaviour of turbulence pa-
rameters near a wall [4, 8, 22, 39, 43, 81]. Following Hanjalic & Launder [22],
fluctuating velocity components can be represented in the following way as
y → 0.
u + rms = a ∗ y + y +
+ O
2
v + rms = b ∗ y +
2 y +
+ O
3
(3.44)
where a and b are constants, and u + rms and v + rms are root-mean-square aver-
aged values.
These relationships are supported by the DNS results of Kim et. al. [30].
As Suga [77] points out:
2
u + 2
= a ∗ y +
2 y +
+ O
4
2
v + 2
= b ∗ y +
4 y +
+ O
6
〈uv〉 + = 〈ab〉 ∗ y +
3 y +
+ O
4
(3.45)
Thus the near-wall behaviour of 〈u 2 〉 is expected to be dominated by a curve