Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 212

Figure 4.11. Frequency distribution of events detected by different
methods, compared to the Gaussian relation [4.2]

4.4. Quadrant-based structure of the Reynolds shear
stress

The contribution of the quadrant i I , II .. to the total =

stress is defined by

∑
∑

uv

[4.3]

c =

i

i

uv

where the numerator is the sum of the stresses when the
event u , v belongs to the quadrant i , and the denominator is
the sum in all the quadrants.

The distributions

c in the inner sublayer

y +

at

< 100

shown in Figure 4.12 correspond closely to the
results of the direct numerical simulations performed by
Kim et al. [KIM 87] at . We can see that the
contributions of the interactions and are slight. The
contribution of the ejections in quadrant ( ) is
predominant at , while in the lower buffer and viscous
sublayers, sweeps of quadrant

Re

τ =

500

Re

τ =

180
I

III
II

u < 0, v > 0

y + > 12

( ) predominate IV

u > 0, v < 0

(see Figure 4.13).