Large- and Very Large-scale Structures - Transport and Coherent Structures in Wall Turbulence - page 389

incoherent turbulence, rather than by coherent streamwise
organization of the vortices. There is a certain similarity to
be seen between the suggestion made by these authors and
the model advanced by Landahl (see section 5.4). However, it
is possible to point out certain nuances and important
differences. The group led by Jiménez suggests that the
packets and their wakes are linear objects, convected by the
mean local velocity, and diffusing by the effect of the
turbulent viscosity in the logarithmic sublayer.

These hypotheses are reduced to a simple advection/diffusion
transport equation for the streamwise vorticity

+ +

ν = κ y

t

. The size
of a compact structure v increases linearly over time in all
spatial directions [ALA 06a].

ω

x

The conditional velocity field corresponding to the
attached structures resembles the field observed in the
packets of HPV s (Figure 6.8). Figure 6.12, which is taken
from [ALA 06b], is curiously similar to the double cones
originally proposed by Townsend [TOW 76] (Figure 5.8,
p. 157), which is reproduced at the top of Figure 6.12. The
low-velocity streak

in the wake is considerably long in
comparison to the pocket

u < 0

that surrounds the packet. u > 0

6.5. Regeneration of the packets

The model proposed by Landahl [LAN 90], which is
discussed in detail in section 5.4, constitutes the basis to
provide an explanation - if only a qualitative one - for the
regeneration of the packets of structures. Remember that
Landahl [LAN 90] uses the highly intermittent nature of the
fluctuations in wall-normal velocity, and rewrites the
transport equation for v in the form of relation [5.27], i.e.

2 2

Dv vU Qxyz tt
Dt

∇ ∂∂

( ) ( )

[6.1]

− = ,, δ −

2 n n

∂∂ x y