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# Exploiting the Turbulence Energy Cascade for Flow Visualization

## Armin Pobitzer

### Abstract

Even though modern technology and tools, together with available computer power, theoretically enable us to visualise large vector fields directly, it often is neither interesting nor necessary to visualise every detail of them. Usually, interesting features of the investigated field can be visualized more efficiently using dedicated feature detectors, e.g. the $\lambda_2$ criterion [2] for vertical structures. In settings with highly complex flow patterns, such as fully developed turbulence, feature detectors may, however, mark almost the whole flow domain as a feature. In these cases visualisations based on these detectors become hard to interpret due to occlusion and visual cluttering. This problem is well known in visualisation, and has been addressed by previous work. Many of these methods have in common that they extract all features at first, and discard some of them afterwards. Criteria for this discarding are often of geometrical character, such as size (volume, length, area ...) or distance to next feature. While the visual output of such strategies satisfies the need to reduce occlusion and visual clutter, the interpretability of the results remains an open question. The immediate relation between the velocity field and the output of the feature detector is lost, since the simplication is made on the image-level' only. In this talk we discuss how the internal structure of flow fields can be exploited, in particular the turbulence energy cascade. Based on proper orthogonal decomposition [3], we present a general simplification scheme for feature extraction that preserves the 1-to-1 relation between visual output of the method and the flow pattern it is extracted from. We apply the simplification scheme on both Eulerian and Lagrangian feature detectors and discuss the results. In particular the impact of the simplification scheme on the detection and visualization of Lagrangian Coherent Structures based on Finite-time Lyapunov exponents is addressed. The results presented in this talk are published in the article Energy-scale Aware Feature Extraction for Flow Visualization [4]. [1] L. Hesselink, J. Helman, and P. Ning, Quantitative image processing in fluid mechanics, Experimental Thermal and Fluid Science, 5 (1992), pp. 605-616. Special Issue on Experimental Methods in Thermal and Fluid Science. [2] J. Jeong and F. Hussain, On the identification of a vortex, Journal of Fluid Mechanics, 285 (1995), pp. 69-84. [3] J. L. Lumley, The structure of inhomogeneous turbulent flows, in Atmospheric Turbulence and Radio Wave Propagation, Elsevier, 1967, pp. 166-178. [4] A. Pobitzer, M. Tutkun, O Andreassen, R. Fuchs, R. Peikert, and H. Hauser, Energy-scale aware feature extraction for flow visualization, Computer Graphics Forum, 30 (2011), pp. 771-780. [5] F. Sadlo and R. Peikert, Visualizing Lagrangian coherent structures: A comparison to vector field topology, in Topology-Based Methods in Visualization II: Proc. of the 2nd TopoInVis Workshop (TopoInVis 2007), H.-C. Hege, K. Polthier, and G. Scheuermann, eds, 2009, pp. 15-29.

### Published

Invited talk at the weekly seminar of Laboratoire de M\'ecanique de Lille

• Location: Lille, France
• Date: February 2012

### BibTeX

@misc{Pobitzer12Exploiting,
author = {Armin Pobitzer},
title  ={Exploiting the Turbulence Energy Cascade for Flow Visualization},
year = {2012},
month = {February},
howpublished = {Invited talk at the weekly seminar of Laboratoire de M\'{e}canique de Lille},
location = {Lille, France},
abstract = {Even though modern technology and tools, together with available
computer power, theoretically enable us to visualise large vector fields
directly, it often is neither interesting nor necessary to visualise
every detail of them. Usually, interesting features of the investigated
field can be visualized more efficiently using dedicated feature
detectors, e.g. the $\lambda_2$ criterion [2] for vertical structures.

In settings with highly complex flow patterns, such as fully developed
turbulence, feature detectors may, however, mark almost the whole flow
domain as a feature. In these cases visualisations based on these
detectors become hard to interpret due to occlusion and visual
cluttering. This problem is well known in visualisation, and has been
addressed by previous work. Many of these methods have in common that
they extract all features at first, and discard some of them afterwards.
Criteria for this discarding are often of geometrical character, such
as size (volume, length, area ...) or distance to next feature. While
the visual output of such strategies satisfies the need to reduce
occlusion and visual clutter, the interpretability of the results
remains an open question. The immediate relation between the velocity
field and the output of the feature detector is lost, since the
simplication is made on the image-level' only.

In this talk we discuss how the internal structure of flow fields can be
exploited, in particular the turbulence energy cascade. Based on proper
orthogonal decomposition [3], we present a general simplification
scheme for feature extraction that preserves the 1-to-1 relation between
visual output of the method and the flow pattern it is extracted from.
We apply the simplification scheme on both Eulerian and Lagrangian
feature detectors and discuss the results. In particular the impact of
the simplification scheme on the detection and visualization of
Lagrangian Coherent Structures based on Finite-time Lyapunov exponents
is addressed. The results presented in this talk are published in the
article Energy-scale Aware Feature Extraction for Flow Visualization
[4].

[1] L. Hesselink, J. Helman, and P. Ning, Quantitative image processing
in fluid mechanics, Experimental Thermal and Fluid Science, 5 (1992),
pp. 605-616. Special Issue on Experimental Methods in Thermal and Fluid
Science.

[2] J. Jeong and F. Hussain, On the identification of a vortex, Journal of
Fluid Mechanics, 285 (1995), pp. 69-84.

[3] J. L. Lumley, The structure of inhomogeneous turbulent flows, in
Atmospheric Turbulence and Radio Wave Propagation, Elsevier, 1967, pp.
166-178.

[4] A. Pobitzer, M. Tutkun, O Andreassen, R. Fuchs, R. Peikert, and H.
Hauser, Energy-scale aware feature extraction for flow visualization,
Computer Graphics Forum, 30 (2011), pp. 771-780.

[5] F. Sadlo and R. Peikert, Visualizing Lagrangian coherent structures:
A comparison to vector field topology, in Topology-Based Methods in
Visualization II: Proc. of the 2nd TopoInVis Workshop (TopoInVis 2007),
H.-C. Hege, K. Polthier, and G. Scheuermann, eds, 2009, pp. 15-29.},

url = {http://lml.univ-lille1.fr/lml/?page=33&seminID=172},

}