Civil Engineering Reference
In-Depth Information
The criterion can offer an acceptable detection of
wall structures, as indicated previously. However, it may
give rise to inadequate detection in certain configurations.
Jeong and Hussain [JEO 95] give a few relevant examples of
this, one of which we present in this section. Consider a
swirling jet with conical symmetry, which is a source of axial
momentum and recirculation concentrated at the origin. The
flow is associated with a significant helical motion
(Figure 3.24) and with canonical symmetry, such as the
vortex associated therewith. The application of the criterion
reveals two vortex cores: the first around the axis that
truly corresponds to the real conical vortex, but also a second
detached zone, shown in Figure 3.27(b), which is an artifact
caused by the detection technique. The invariant is also
negative in proximity to the axis, and becomes positive
beyond it. The criterion , therefore, “lacks” the axis of
the vortex where the vorticial rotation is practically as great
as that of a rigid body. The “lambda-2” criterion introduced
by Jeong and Hussain [JEO 95], which we will analyze later
on, proves more effective in the configuration shown in
Figure 3.27, as well as in other situations (mixing layer,
circular jet and axial vortex ring).
Δ=
0
Δ>
0
Q
Q
>
0
3.7. Pressure field and vortices
The pressure tends toward a local minimum at the vortex
core in a steady, non-viscous 2D flow. It is a direct
consequence of the cyclostrophic equilibrium, between the
centrifugal force and the force of pressure. Take the example
of a circular vortex
15
whose vorticity is singular
16
with
for
and
outside of the cylinder
. The
ω
z
= ω
0
ω
z
=
0
<
a
>
a
r
r
tangential velocity distribution is
in the vortex
v
θ
= ω
0
r
2
and
θ
= ω
0
a
2
outside of it (
r > a
). The cyclostrophic
v
2
r
15 Rankine vorticial filament.
16 The location
ra
is the singular point in the vortex where there is a
jump in vorticity. For example, see [SAF 92].
=
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