Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 72

Figure 2.3. Relationship between production and dissipation of kinetic
energy in a fully developed turbulent channel flow, according to the DNS
performed by Bauer [BAU 14]

Figure 2.3 shows the ratio P K + ε *+ in a fully-developed
turbulent channel flow for four Reynolds numbers ranging
from low,

Re τ = 180 , to moderate, Re τ = 1100 . To begin with,

we see that the structural parameter P K +

+ is remarkably
independent of the Reynolds number, in the zone y + <

*

ε

K

50 . The
zone wherein the P K + ε *+ ratio remains close to 1 extends
when the Reynolds number increases. However, production
is not exactly equal to dissipation, and P K + ε *+ increases
slightly in the “candidat e” sublayer for the universal
logarithmic distribution of U + y +

( )

. The maximum Reynolds

number achieved with the DNS in Figure 2.3 is,

of course, not sufficiently high to deliver a logarithmic
sublayer with the universal von Kárman constant. 7

Re

τ =

1, 1 0 0

7 See the brief discussion given in Chapter 1 and [TAR 11b].