Civil Engineering Reference
In-Depth Information
Remember that the discriminant divides the
topological domain into two: contains the focal
structures (stable or unstable), while, on the other side,
covers the critical points such as nodes-saddle points
(Figure 3.19). The invariant , therefore, seems to be an
appropriate scalar to describe coherence in a wall-bounded
flow. Figure 3.24, adapted from [CHA 00], shows a bird's-eye
view of the isosurfaces in a turbulent boundary layer at
.
12
The mean flow is in the direction. The white
spaces coincide with the critical points such as node-saddle
point, and the gray structures encompass the focal points
. We can see that the structures are clearly defined from
a topological point of view: they occupy a significant amount
of space, they are compact and elongated in the direction of
the flow. We can also see the heads of certain hairpin
vortices that are bounded by rectangles in Figure 3.24. The
intense zones of negative Reynolds stresses are
adjacent to the structures detected by (the dark-shaded
zones in Figure 3.25). However, zones of significant positive
stresses are also contained in regions close to the
isosurfaces of the discriminant, and it is difficult to establish
a clear connection between the highly active structures that
engender Reynolds stresses and regions . Chacin
and Cantwell
[CHA 00] observe that zones where reaches
one of its extreme values (maximum or minimum), with
particularly significant gradients, coincide with active
regions with great production of Reynolds stresses. The high-
energy zones are also juxtaposed with the structures
. What clearly emerges from the results found by
Chacin and Cantwell [CHA 00] is that the zones are
completely devoid of any significant kinetic energy, and in
that sense they are primarily under the influence of
passive st
ru
ctures that do not contribute (or contribute only
little) to
Δ=
0
Δ>
0
Δ<
0
Δ
Δ=
0
Re
θ
=
670
x
Δ>
0
uv
+
<
0
Δ=
0
uv
+
>
0
uv
−
>
0
Δ>
0
Δ
u
i
u
i
Δ>
0
Δ<
0
.
−
uv
12 Direct numerical simulations performed by Spallart [SPA 88].
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