Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 303

[HAR 89] considers that the production of is

intermittent and takes place only during the bursts. 10 He
assumes that

− uv

Δ t

2 2

Dl 1 Dl

er

∫

2

= dt = f n l [5.44]

er e m

2

Dt Δ t Dt

er 0

is the frequency of the bursts,
n is the mean number of individual ejections per burst and
l

In this relation,

f =Δ 1 t

er er

is the classic Prandtl mixing length. The distribution
of the Reynolds stress in inner variables is therefore

+ +

= κ y

+

1
2

∂
∂

U + + + 2

[5.45]

−= uv f n l

er e m

y

+

f + , this equation connects the near-wall
turbulent activity to the Reynolds stress, if only
conceptually. It also offers an acceptable prediction of the
distribution of

By way of

er

uv + in the inner sublayer, despite the

simplicity of the model.

−

5.5. Elongated structures and streak formation

QSVs are structures which are greatly elongated in
direction x . They give rise to high- and low-velocity streaks
by way o f an advection mechanism. Transport by the
term is a characteristic example of streamwise

advection [ELL 75]. A convincing proof establishing the role
of advection in streak formation is given by Hamilton et al.
[HAM 95]. These authors analyzed the regeneration

− vU y ∂∂

10 The bursts are groups of ejections. They are linked to the cluster of
coherent structures (see Chapter 6).