Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-27T00:11:24.323Z Has data issue: false hasContentIssue false
  • English
  • Français

Detection of Lagrangian coherent structures in three-dimensional turbulence

Published online by Cambridge University Press:  23 January 2007

M. A. GREEN ,
C. W. ROWLEY  and
G. HALLER
M. A. GREEN
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
C. W. ROWLEY
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
G. HALLER
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We use direct Lyapunov exponents (DLE) to identify Lagrangian coherent structures in two different three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. We find that despite additional computational cost, the DLE method has several advantages over Eulerian methods, including greater detail and the ability to define structure boundaries without relying on a preselected threshold. As a further advantage, the DLE method requires no velocity derivatives, which are often too noisy to be useful in the study of a turbulent flow. We study the evolution of a single hairpin vortex into a packet of similar structures, and show that the birth of a secondary vortex corresponds to a loss of hyperbolicity of the Lagrangian coherent structures.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 111 - 120
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.CrossRefGoogle Scholar
Haller, G. 2001 Distinguished material surfaces and coherent structures in 3D fluid flows. Physica D 149, 248–277.CrossRefGoogle Scholar
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14 (6), 1851–1861.CrossRefGoogle Scholar
Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 1–26.CrossRefGoogle Scholar
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two dimensional turbulence. Physica D 147, 352–370.CrossRefGoogle Scholar
Head, M. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Rep. CTR-S88.Google Scholar
Jeong, J. & Hussein, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Koh, T. Y. & Legras, B. 2002 Hyperbolic lines and the stratospheric polar vortex. Chaos 12 (2), 382–394.CrossRefGoogle ScholarPubMed
Lapeyre, G. 2002 Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. Chaos 12 (3), 688–698.CrossRefGoogle ScholarPubMed
Lekien, F. & Leonard, N. 2004 Dynamically consistent Lagrangian coherent structures. In AIP: 8th Experimental Chaos Conference, CP 742, pp. 132–139.Google Scholar
Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J. E. & Swinney, H. L. 2006 Uncovering the lagrangian skeleton of turbulence. Phys. Rev. Lett. (submitted).CrossRefGoogle Scholar
Shadden, S., Dabiri, J. & Marsden, J. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105-1–047105-11.CrossRefGoogle Scholar
Shadden, S., Lekien, F. & Marsden, J. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensinal aperiodic flows. Physica D 212, 271–304.CrossRefGoogle Scholar
Smith, C. & Walker, J. 1991 On the dynamics of near-wall turbulence. In Turbulent Flow Structure Near Walls (ed. Walker, J.). The Royal Society (First published in Phil. Trans. R. Soc. Lond. A 336, 1991).Google Scholar
Theodorsen, T. 1955 The structure of turbulence. In 50 Jahre Grenzschichtforschung (ed. Görtler, H. & Tollmien, W.). Vieweg and Sohn.Google Scholar
Voth, G. A., Haller, G. & Gollub, J. P. 2002 Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 88, 254501.CrossRefGoogle ScholarPubMed
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar