Abstract
The lack of a universally accepted mathematical definition of a vortex structure has led to a considerable number of Eulerian criteria to identify coherent structures. Most are derived from the instantaneous local velocity gradient tensor and its derivatives and require appropriate thresholds to extract the boundaries of the structures. Notwithstanding their great potential for studying coherent structures, most criteria are not frame-independent and they lack a clear physical meaning. The Lyapunov exponent, a popular tool in dynamical system theory, appears as a promising alternative. This Lagrangian criterion does not suffer from the drawbacks of the Eulerian criteria and is constructed on a simple physical interpretation that includes information on the history of the flow. However, since the computation of the Lyapunov exponent involves the knowledge of fluid particle trajectories, experimental applications are currently restricted to laminar flows and two-dimensional turbulence, provided that velocity fields are time-resolved. In this work, we explore temporal post-treatment methods to extract vortical structures developing in a flow through a smooth axisymmetric constriction. Data from planar time-resolved Particle image velocimetry, measuring two or three components of the velocity vectors, are transformed via the Taylor hypothesis to quasi-instantaneous three-dimensional velocity field and are interpreted in terms of the discrete wavelet decomposition, the finite-time Lyapunov exponent, and the linear stochastic estimation. It appears that these methods can concurrently provide very rich and complementary scalar fields representing the effects of the vortical structures and their interactions in the flow.
Similar content being viewed by others
References
Addison PS (2002) The illustrated wavelet transform handbook. Institute of Physics Publishing, Bristol
Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluids 39:159–169
Adrian RJ, Moin P (1988) Stochastic estimation of organized turbulent structure: homogeneous shear flow. J Fluid Mech 190:531–559
Adrian RJ, Christensen KT, Liu ZC (2000a) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29:275–290
Adrian RJ, Meinhart CD, Tomkins CD (2000b) Vortex organization in the outer region of the turbulent boundary layer. J Fluid Mech 422:1–54
Chakraborty P, Balachandar S, Adrian RJ (2005) On the relationship between local vortex identification schemes. J Fluid Mech 535:189–214
Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids 2:765–777
Christensen KT, Adrian RJ (2001) Statistical evidence of hairpin vortex packets in wall turbulence. J Fluid Mech 431:433–443
Dubief Y, Delcayre F (2000) On coherent-vortex identification in turbulence. J Turbulence 1:1–22
Farge M (1992) Wavelet transforms and their application to turbulence. Annu Rev Fluid Mech 24:395–457
Ganapathisubramani B, Lakshminarasimhan K, Clemens NT (2007) Determination of complete velocity gradient tensor by using cinematographic stereoscopic PIV in a turbulent jet. Exp Fluids 42:923–939
Garth C, Gerhardt F, Tricoche X, Hagen H (2007) Efficient computation and visualization of coherent structures in fluid flow applications. IEEE Trans Vis Comput Gr 13:1464–1471
Green MA, Rowley CW, Haller G (2007) Detection of lagrangian coherent structures in three-dimensional turbulence. J Fluid Mech 572:111–120
Haller G (2001) Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149:248–277
Hunt JCR, Wray AA, Moin P (1988) Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88, Center for Turbulence Research, Stanford
Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94
Koh TY, Legras B (2002) Hyperbolic lines and the stratospheric polar vortex. Chaos 12:382–394
Lapeyre G (2002) Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. Chaos 12:688–698
Mallat S (1999) A wavelet tour of signal processing. Academic Press, London
Marassi M, Castellini P, Pinotti M, Scalise L (2004) Cardiac valve prosthesis flow performances measured by 2D and 3D-stereo particle image velocimetry. Exp Fluids 36:176–186
Mathur M, Haller G, Peacock T, Ruppert-Felsot JE, Swinney HL (2007) Uncovering the Lagrangian skeleton of turbulence. Phys Rev Lett 98(14):144502
Matsuda T, Sakakibara J (2005) On the vortical structure in a round jet. Phys Fluids 17(2):025106
Merzkirch W (1987) Flow Visualization. Academic Press, London
Prasad AK, Adrian RJ (1993) Stereoscopic particle image velocimetry applied to liquid flows. Exp Fluids 15:49–60
Prasad AK, Jensen K (1995) Scheimpflug stereocamera for particle image velocimetry in liquid flows. Appl Optics 34:7092–7099
Rinoshika A, Zhou Y (2005) Orthogonal wavelet multi-resolution analysis of a turbulent cylinder wake. J Fluid Mech 524:229–248
Robinson SK (1991) Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech 23:601–639
Shadden SC, Lekien F, Marsden JE (2005) Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212:271–304
Soloff SM, Adrian RJ, Liu ZC (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8:1441–1454
Sreenivasan KR, Strykowski PJ (1983) An instability associated with a sudden expansion in a pipe flow. Phys Fluids 26:2766–2768
van Doorne CWH, Westerweel J (2007) Measurement of laminar, transitional and turbulent pipe flow using stereoscpic-PIV. Exp Fluids 42:259–272
Vétel J, Garon A, Pelletier D, Farinas MI (2008) Asymmetry and transition to turbulence in a smooth axisymmetric constriction. J Fluid Mech 607:351–386
Vétel J, Garon A, Pelletier D (2009) Lagrangian coherent structures in the human carotid artery bifurcation. Exp Fluids 46:1067–1079
Voth GA, Haller G, Gollub JP (2002) Experimental measurements of stretching fields in fluid mixing. Phys Rev Lett 88(25):254501
Zaman KBMQ, Hussain AKMF (1981) Taylor hypothesis and large-scale coherent structures. J Fluid Mech 112:379–396
Zhou J, Adrian RJ, Balachandar S (1996) Autogeneration of near wall vortical structure in channel flow. Phys Fluids 8:288–291
Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387:353–396
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vétel, J., Garon, A. & Pelletier, D. Vortex identification methods based on temporal signal-processing of time-resolved PIV data. Exp Fluids 48, 441–459 (2010). https://doi.org/10.1007/s00348-009-0749-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-009-0749-8