Civil Engineering Reference
In-Depth Information
as discussed in section 3.7. Jeong and Hussein [JEO 95],
therefore, propose to consider only the eigenvalues in
2 2
BS A
[3.65]
=+ =
SS
+
AA
ik
kj
ik
kj
to determine the local minimum of the Hessian tensor
(
(
)
)
. As recalled at the beginning of this
section, the descending eigenvalues of are
real, and we need to determine the group of eigenvalues
including two negative values. The core of the vortex is,
therefore, determined on the basis of the criterion in
accordance with this arrangement. In practice, the detection
requires a threshold , upon which the number and
intensity of the identified structures are necessarily
dependent.
2
−
1
ρ∂∂∂
HPx
x
i
j
(
)
B
λ
1
B
,
λ
2
B
,
λ
3
B
λ
2
B
<
0
λ
2
B
< ς
λ 2
We can obtain a relation between the eigenvalues in
B
and the invariant
. Indeed, equation [3.28] indicates that
Q
1
1
1
(
)
(
)
2
2
2
[3.66]
Qtr
=−
J
=−
tr
S
+
A
S
=−
λλ λ
+
+
1
B
2
B
3
B
2
2
2
for an incompressible flow. The eigenvalues and are
negative. Therefore, the “lambda-2” technique coincides with
the criterion in the zones , although no
clear and definitive correspondence can be established
between the two detection methods, as we will see in detail
later on in this chapter. detection is, in a way, similar to
the technique proposed in [HUN 88] because it is built to
detect vorticity contributions to the pressure minima.
λ
λ
2
B
3
B
Q
>
0
λ
1
B
< λ
+ λ
2
B
3
B
λ
2
3.11. Relations between the topological invariants and
the
technique
λ
2
Chacin and Cantwell
[CHA 00] showed that there are no
direct relations between the
detection method and the
λ
2
Search WWH ::
Custom Search