Exploiting the Turbulence Energy Cascade for Flow Visualization

Armin Pobitzer

MISC, February, 2012

• www

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
• URL: http://lml.univ-lille1.fr/lml/?page=33&seminID=172

Media

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},


}