<s>
In	O
scientific	B-Application
visualization	I-Application
,	O
a	O
vortex	B-Application
core	I-Application
line	I-Application
is	O
a	O
line-like	O
feature	O
tracing	O
the	O
center	O
of	O
a	O
vortex	B-Application
with	O
in	O
a	O
velocity	O
field	O
.	O
</s>
<s>
Several	O
methods	O
exist	O
to	O
detect	O
vortex	B-Application
core	I-Application
lines	I-Application
in	O
a	O
flow	O
field	O
.	O
</s>
<s>
studied	O
and	O
compared	O
nine	O
methods	O
for	O
vortex	B-Application
detection	O
,	O
including	O
five	O
methods	O
for	O
the	O
identification	O
of	O
vortex	B-Application
core	I-Application
lines	I-Application
.	O
</s>
<s>
One	O
of	O
these	O
five	O
methods	O
is	O
by	O
:	O
in	O
a	O
velocity	O
field	O
v(x,t )	O
a	O
vector	O
x	O
lies	O
on	O
a	O
vortex	B-Application
core	I-Application
line	I-Application
if	O
v(x,t )	O
is	O
an	O
eigenvector	O
of	O
the	O
tensor	O
derivative	O
and	O
the	O
other	O
–	O
not	O
corresponding	O
–	O
eigenvalues	O
are	O
complex	O
.	O
</s>
