3D acoustic Lagrangian velocimetry

  • M. Bourgoin
  • P. Gervais
  • A. Cartellier
  • Y. Gagne
  • C. Baudet
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 11)


We report Lagrangian measurements obtained with an acoustic Doppler velocimetry technique. From the Doppler frequency shift of acoustic waves scattered by tracer particles in a turbulent flow, we are able to measure the full three-component velocity of the particles. As a first application, we have studied velocity statistics of Lagrangian tracers in a turbulent air jet at R λ ∼ 320 and at various distances from the nozzle. The choice of an air jet is motivated by the fact that jets produce a well characterized high level turbulence and open air flows are well suited to simultaneously achieve classical hot wire Eulerian measurements. Therefore, we are also able to explicitly address the question of the differences between Eulerian and Lagrangian statistics. As Lagrangian tracers we use soap bubbles inflated with Helium which are neutrally buoyant in air and can be assimilated to fluid particles. Velocity statistics are analyzed. We show that the Lagrangian autocorrelation decays faster in time than its Eulerian counterpart.


Doppler Frequency Shift Integral Length Scale Probability Density Function Soap Bubble Lagrangian Statistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Virant, M., and Dracos, T., 1997. 3D PTV and its application on Lagrangian motion. Measurement science and technology, 8, pp. 1539–1552CrossRefGoogle Scholar
  2. [2]
    Ott, S., and Mann, J., 2000. An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. Journal of Fluid Mechanics, 422, pp. 207–223CrossRefGoogle Scholar
  3. [3]
    LaPorta, A., Voth, G. A., Crawford, A. M., Alexander, J., and Bodenschatz, E., 2002. Fluid particle accelerations in fuly developped turbulence. Nature, 409, February, p. 1017CrossRefGoogle Scholar
  4. [4]
    Bourgoin, M., Ouellette, N. T., Xu, H., Berg, J., and Bodenschatz, E., 2006. The role of pair dispersion in turbulent flow. Science, 311, February, p. 835CrossRefGoogle Scholar
  5. [5]
    Xu, H., Bourgoin, M., Ouellette, N. T., and Bodenschatz, E., 2006. High order Lagrangian velocity statistics in turbulence. Physical Review Letters, 96, January, p. 024503CrossRefGoogle Scholar
  6. [6]
    Mordant, N., Metz, P., Michel, O., and Pinton, J.-F., 2001. Measurement of Lagrangian velocity in fully developed turbulence. Physical Review Letters, 87(21), p. 214501CrossRefGoogle Scholar
  7. [7]
    Sato, Y., and Yamamoto, K., 1987. Lagrangian measurement of fluid-particle motion in an isotropic turbulent field. Journal of Fluid Mechanics, 175, pp. 183–199CrossRefGoogle Scholar
  8. [8]
    Wygnanski, I., and Fiedler, H., 1969. Some measurements in the self-preserving jet. Journal of Fluid Mechanics, 38(3), pp. 577–612CrossRefGoogle Scholar
  9. [9]
    Pope, S. B., 2000. Turbulent flows. Cambridge University PressGoogle Scholar
  10. [10]
    Tennekes, H., and Lumley, J. L., 1992. A first course in turbulence. MIT pressGoogle Scholar
  11. [11]
    Voth, G. A., la Porta, A., Crawford, A. M., Alexander, J., and Bodenschatz, E., 2002. Measurement of particle accelerations in fully developed turbulence. Journal of Fluid Mechanics, 469, pp. 121–160CrossRefGoogle Scholar
  12. [12]
    Poulain, C., Mazellier, N., Gervais, P., Gagne, Y., and Baudet, C., 2004. Spectral vorticity and Lagrangian velocity measurements in turbulent jets. Flow, Turbulence and Combustion, 72, pp. 245–271CrossRefGoogle Scholar
  13. [13]
    Flandrin, P., 1993. Temps-frequence. HermesGoogle Scholar
  14. [14]
    Taylor, 1921. Diffusion by continuous movements. Proc. London Math. Soc., 20, p. 196CrossRefGoogle Scholar
  15. [15]
    Lipari, G., Apsley, D. D., and Stansby, P. K., 2006. Numerical particle tracking studies in a turbulent jet. in the present Proceedings of Euromech Colloquim 477Google Scholar
  16. [16]
    Batchelor, 1957. Diffusion in free turbulent shear flows. Journal of Fluid Mechanics, 3, pp. 67–80CrossRefGoogle Scholar
  17. [17]
    Yeung, P. K., 2002. Lagrangian investigations of turbulence. Annual Review of Fluid Mechanics, 34, pp. 115–142CrossRefGoogle Scholar
  18. [18]
    Corrsin, S., 1963. Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. Journal of the Atmospheric Sciences, 20(2), pp. 115–119CrossRefGoogle Scholar
  19. [19]
    Kraichnan, R. H., 1964. Relation between Lagrangian and Eulerian correlation times of a turbulent velocity field. Physics of Fluids, 7(1), pp. 142–143CrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • M. Bourgoin
    • 1
  • P. Gervais
    • 2
  • A. Cartellier
    • 1
  • Y. Gagne
    • 1
  • C. Baudet
    • 1
  1. 1.L.E.G.I. - U.M.R. 5519 - C.N.R.S. / I.N.P.G. / U.J.F.Grenoble Cedex 09France
  2. 2.L.E.A. - U.M.R. 6609 - C.N.R.S. / Universit de PoitiersFuturoscope Chasseneuil CedexFrance

Personalised recommendations