Measuring Invariant (Frame Independent) Quantities Composed of Velocity Derivatives in Turbulent Flows

  • A. Tsinober
  • E. Kit
  • T. Dracos


This is a presentation of results of experiments on a turbulent grid flow and few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was achieved by a 12 hot-wire probe (3 arrays x 4 wires), produced for this purpose using specially made equipment (micromanipulators, etc.), calibration unit and calibration procedure. The probe has no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results. Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate of strain tensor and the positiveness of the total enstrophy generating term even for rather short events. Emphasis is placed on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference, as the most appropriate to describe physical processes. From the methodical point of view the main result is that the multi-hotwire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least, at moderate Reynolds numbers.


Calibration Procedure Probability Density Distribution Wire Array Invariant Quantity Moderate Reynolds Number 
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. Ashurst, Wm. T., Kerstein, A.R., Kerr, R.A. & Gibson, C.H. 1987. Phys. Fluids, 30, 2343–2353.CrossRefADSGoogle Scholar
  2. Arora, S.C. & Azad, R.S. 1980. J. Fluid Mech., 97, 385–404.CrossRefADSGoogle Scholar
  3. Balint, J.L., Vukoslavcevic, P. & Wallace, J.M. 1987. In Advances in Turbulence (eds. G. Compte-Bellot and J. Mathieu) ( Springer, Berlin ), pp. 456–464.CrossRefGoogle Scholar
  4. Betchov, R. 1956. J. Fluid Mech. 1, 497–504.CrossRefMATHADSMathSciNetGoogle Scholar
  5. Chen, H., Herring, J.R., Kerr, R.M. & Kraichnan, R.H. 1989. Phys. Fluids A1, 1844–1854.CrossRefMATHADSGoogle Scholar
  6. Corrsin, S. & Fournier, J.L. 1982. Phys. Fluids, 25, 583–585.CrossRefMATHADSGoogle Scholar
  7. Dracos, T., Kholmyansky, M., Kit, E. & Tsinober A. 1990. In Proceedings of the IUTAM Symposium on Topological Fluid Mechanics, Cambrdige, U.K., August 13–18, 1989. (eds. H.K. Moffat and A. Tsinober, Cambr. Univ. Press ), pp. 564–584.Google Scholar
  8. Frenkiel, F.N., Klebanoff, P.S. & Huang T.T. 1979. Phys. Fluids, 22, 1606–1617.CrossRefADSGoogle Scholar
  9. Kerr, R.M. 1985. J. Fluid Mech., 153, 31–58.CrossRefMATHADSGoogle Scholar
  10. Kit, E., Tsinober, A., Teitel, M., Balint, J.L., Wallace, J.M. & Levich, E. 1988. Fluid Dyn. Res., 3 pp. 289–294.CrossRefADSGoogle Scholar
  11. Kraichnan, R. & Panda, R. 1988. Phys. Fluids 31, 2395–2397.CrossRefMATHADSGoogle Scholar
  12. Narasimha, R. 1990. In Turbulence at the Cross Roads, (ed. J.L. Lumley ), Springer, pp. 13–48.Google Scholar
  13. Siggia, E. 1981. J. Fluid Mech. 107, 375–406.CrossRefMATHADSGoogle Scholar
  14. Shtilman, L. & Polifke, W. 1989. Phys. Fluids, A1, 778–780.CrossRefADSGoogle Scholar
  15. Taylor, G.I. 1938. Proc. Roy. Soc. A164, 15–23.CrossRefMATHADSGoogle Scholar
  16. Tennekes, H. & J.L. Lumley, J.L. 1974 A first course in turbulence. MIT Press, 87–90.Google Scholar
  17. Townsend, A.H. 1951. Proc. Roy. Soc. London, A208, 534–542.CrossRefMATHADSGoogle Scholar
  18. Tsinober, A. 1988 Multi-hot-wire probe production for measurement of all nine velocity gradient. Int. Rep. Fac. Engn., Tel-Aviv Univ.Google Scholar
  19. Tsinober, A. 1990. Phys. Fluids, 2A, 484–486.CrossRefMATHADSMathSciNetGoogle Scholar
  20. Tsinober, A., Kit, E. & Dracos, T. 1990 Experimental study of velocity derivatives in turbulent grid and boundary layer flows, submitted to the J. Fluid Mech.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1991

Authors and Affiliations

  • A. Tsinober
    • 1
    • 2
  • E. Kit
    • 1
    • 2
  • T. Dracos
    • 2
  1. 1.Institut für Hydromechanik und WasserwirtschaftETH - HonggerbergZürichSwitzerland
  2. 2.Department of Fluid Mechanics, Faculty of EngineeringTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations