Vortex detection in time-dependent flow

Ronny PeikertETH Zurich

Vortex detection - early work

• Derived from physical properties:– vortex regions:

• Pressure Laplacian• Q criterion (Okubo-Weiss, Hunt 1991)

• 2 criterion (Jeong and Hussain, 1995)

– vortex axes (vortex core lines): • Pressure&vorticity based (Banks and Singer, 1994) • Pressure valley line (Kida and Miura, 1997)

These are valid for steady and unsteady flow!

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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Vortex detection - early work (2)

• Derived from geometric/topological properties: – vortex axes:

• critical point analysis, separatrices (Helman and Hesselink 1991, Globus et al. 1991)

• helicity-based, Levy et al. (1990)• streamline-based, Sujudi and Haimes (1995)• higher-order, Roth and Peikert (1998)

These are just formulated for steady flow!

But vortex axes are useful, complementary to vortex regions!

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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Vortex detection - more recent work

• Lagrangian type methods:

– Non-local swirl [Cucitore 1999]

– Objective criterion Mz [Haller 2005]

Better than 2 ?

• Time-dependent vortex axes methods:

– Swirling particle motion [Weinkauf et al. 2007]

– Work in progress [Bürger et al.]

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007 4

Adaptations of Sujudi-Haimes criterion

• Sujudi-Haimes criterion (in parallel vectors formulation)

AND filter criteria

• Equivalent and more efficiently computable:

AND filter criteria

• Time-dependent version: AND filter criteria

• Weinkauf et al. (2007) (equivalent formulation):

AND filter criteria

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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s a u u

realEigenvectorr ε urε u

sa u

ta u accelerationt t

u

a u u

t ra ε

Tilting vortex example

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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,0,tz z

, ,tz tz z

streamlines at t=0.3 pathlines

seeded at t=0.3

Sujudi-Haimes axis ,0,tz z

, , ,

y tz

x y z t x tz

z

u

Vortex rope example

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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Synthetic vortex rope

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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streamlines

pathlines

Radii of vortex core lines

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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Steady flow Unsteady

flow

Levy et al.

Sujudi /

Haimes

Higher-order

Correct

1

1k

Rs

2

1k k

Rs s

1k

Rs

1

1k

Rs

2

1k k

Rs s

1kR

s

12

kR

s

ad

ap

ted

meth

od

s

Comparisons

Comparison of and :• Both reduce to Sujudi-Haimes criterion if flow is steady.• Criterion is Galilean invariant.• Consequently, it produces Sujudi-Haimes vortex core

lines also in linearly moving frame of reference. • Visually indistinguishable in synthetic vortex rope and

CFD vortex rope examples.• Criterion is possibly better in other CFD dataset

examples.

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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ta u t ra ε

t ra ε

ta u

• Comparison (Tufo et al. '99)

– mean velocity– rms velocity– pressure– spanwise vorticity

– 2

• Vortex core line methods have problems with mixinglayer vortices

• How about Mz ?

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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Comparisons (2)

Conclusion

• Existing methods need further comparison

• What degree of invariance is needed? Galilean? Objective?

• We need a topology of time-dependent vector fields

Dagstuhl Seminar Scientific Visualization, July 15-20, 2007

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