7.7 Turbulence near walls
The characteristic velocity distribution in
turbulent boundary layers in Sec. 7.4
, provided wall
functions expressed as boundary conditions for in Sec. 7.5
and Sec. 7.6
. Boundary
conditions also need to be specified for turbulence fields at solid
walls.
The turbulence generation influences the
distribution of turbulence fields near a wall. At the wall,
.
In the inertial sub-layer,
from Eq. (7.5
) with:
, obtained by combining
Eq. (6.21
) and Eq. (7.15
); and,
Eq. (6.24
).
Since decreases with increasing
in the inertial
sub-layer,
passes through a peak within the buffer layer (at
).
The peak in causes a similar peak
in
, shown in the following diagram. To the left of the peak,
turbulent energy is transported back towards the wall by diffusion
The profile of dissipation
results from
, obtained
from Eq. (7.1
). Very close to the wall
(
),
diffusion is predominately molecular, such that it non-zero at the
wall. The dissipation
also has a non-zero value
at the wall.
Wall functions and turbulence fields
When using a turbulence model, such as the
model described in Sec. 7.1
, boundary conditions must be
specified for
and
at solid walls. The distribution of
,
non-dimensionalised as
, close to the wall is shown below.
At the wall, but it rises quickly
to a peak at
before levelling off at
as
.
With wall functions, the height of the centre of
each near-wall cell should correspond to within the range
.
Viewed at that scale, the
profile appears flat. For
, there is no such
simple profile shape. These observations lead to the boundary
conditions for
and
when using wall functions:
- zero
gradient for
;
- calculated
near-wall cell value for
, according to:
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(7.26) |




