Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 90

the dissipation length scale L

ε K introduced by Hunt et al.
[HUN 87] and [HUN 00]. In a turbulent wall flow with slight
shear (SS), the smallest of the “macro-scales” is that induced
by the wall-normal fluctuating velocity
[HUN 84]. The dissipation is then ap proximately invariant
with y and the turbulent intensity v 2 depends on ε K and y ,

wh ich, when subjected to dimensional analysis, gives us
v 2

2/3 y 2/3 . The di ssi pation length scale with SS is
therefore a function of v 2 and

= C ε

K

ε K

ε K
v 2

−

1

C −3/2 y −1 Ay −1 L ≡ ≡ =

3/2 ε

⎛ ⎞ ⎠

⎜ ⎟

⎝

The value of C in a convective atmospheric boundary
layer is C 2.5 . However, in a turbulent flow with co ns tant

shear without the presence of a wall, L

=

ε K depends on v 2 and

on the mean shear

A dU / dy
v 2
At this point, Hunt advances an interesting physical
interpretation of the dissipation near to a shear flow in the
vicinity of a wall: is due to the deformation of the small
structures by the larger ones, and is controlled by the
significant gradients of the structures containing the energy.
However,

ε −

1

L ≡′

ε K

ε −

1

, and consequently the length scale

ε ∝ L L

ε K K

near to a real wall depends on the less dominant of the two
effects, i.e. on the wall or the shear. Hunt therefore proposes
to consider the harmonic mean of the two expressions

A dU / dy
v 2

L ε −1 Ay −1 ≡ +′

This form was evaluated in the analysis based on the RDT
performed by Lee and Hunt [LEE 89]. This expression
corresponds relatively closely to the DNS data for y + at = 50