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

CHAPTER 3. CHANNEL FLOW 47
y + is plotted against y ∗
v 2 for various values of Reτ in Figure 3.10. There is
reasonable agreement between y + and y ∗
v 2. U + and U ∗
v 2 at various Reynold’s
numbers are plotted in Figure 3.11. The 〈v 2 〉 normalising approach suffers
from the fact that 〈v 2 〉 + tends to zero as y → 0 faster than U + does, so that
U ∗
v 2 becomes large. As y → 0, U + is expected to become proportional to y +
and 〈v2 〉 + becomes proportional to (y + ) 4 U , so +
√
〈v2 +
〉
1
y + .
becomes proportional to