Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 280

To express these relations in terms of the conditions
linked to the self-similar distribution,

()

requires an
asymptotic analysis at the regular singular point

F η

and

η = 0

the irregular point . The boundary conditions η =∞

1 1

() ()

F '0 − ι Re F 0 = Re

Γ Γ

[5.9]

8 8

()

F ∞= 0

established by Pearson and Abernathy [PEA 84] for

α = 0

are also valid when . The differential equation [5.8] can

be solved numerically with no particular difficulty.

α ≠ 0

Here we present a few results obtained for at

Re

Γ =

5

.
The Reynolds number chosen is small in comparison to the
Re

t +

. The dimensionless mean velocity is U

+ + +

=+

= 0.1 y α z

of the streamwise structures in the buffer sublayer, with
the aim being to approximate, as closely as possible, the
expected conditions at the start of the process of
regeneration at particularly short times. We assume that the
effect of the wall is slight for low values of t and distance r .

Γ

Figure 5.3. Local velocity induced by an Oseen vortex of intensity , Re

Γ =

5

t + = z + = at , and (dotted lines), compared with the case 0.1 0 α =± 0.2

where (solid line) α = 0