Advertisement

Order and Disorder in Turbulent Flows

  • John L. Lumley
Conference paper

Abstract

Examination of pictures of turbulent flows reveals a wide range of order and apparent disorder, seeming to depend on the geometry, Reynolds number and initial conditions. The ordered component may arise as the remnant of an instability of the laminar flow that first gave rise to the turbulence, or as an instability of the turbulent profile and transport. Sometimes it is necessary to take the ordered component explicitly into account in a description of the flow (if the ordered component has arisen from a source different from that of the smaller scale, apparently disordered, component), and sometimes it is not necessary, if everything has arisen from the same source, both components are in equilibrium with each other, and there is only one scaling law for both. The disordered component, on the evidence of exact numerical simulations, is deterministic. By analogy with temporal chaos in mechanical systems with small numbers of degrees of freedom, it is tempting to identify it as resulting from a strange attractor, although there is no real evidence for this. The question seems to be of primarily philosophical interest. What evidence there is suggests that at reasonable Reynolds numbers the dynamical structure would in any event be too complex to be computable, nor are we interested in the details. It seems that a statistical approach to the structure in the phase space would make most sense, since we are interested presumably in global statements, bounds, and the like.

Keywords

Reynolds Stress Turbulent Boundary Layer Proper Orthogonal Decomposition Wall Region Drag Reduction 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aubry, N., Holmes, P., Lumley, J. L. and Stone, E. 1988. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192: 115–173.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Stone, E. 1989. A Study of Low Dimensional Models for the Wall Region of a Turbulent Boundary Layer. Ph. D. Thesis. Ithaca, NY: Cornell University.Google Scholar
  3. 3.
    Bloch, A. M. and Marsden, J. E. 1989. Controlling Homoclinic Orbits. Theoretical and Computational Fluid Dynamics. In Press.Google Scholar
  4. 4.
    Lumley, J.L. 1967. The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation, A.M. Yaglom and V.I. Tatarski:, eds.: 166–178. Moscow: Nauka.Google Scholar
  5. 5.
    Love, M. 1955. Probability Theory. New York: Van NostrandGoogle Scholar
  6. 6.
    Lumley, J.L. 1970. Stochastic tools in turbulence. Academic Press, New York.zbMATHGoogle Scholar
  7. 7.
    Lumley, J.L. 1981. Coherent structures in turbulence. Transition and Turbulence, edited by R.E. Meyer, Academic Press, New York: 215–242.Google Scholar
  8. 8.
    Herzog, S. 1986. The large scale structure in the near-wall region of turbulent pipe flow. Ph.D. thesis, Cornell University.Google Scholar
  9. 9.
    Tennekes, H. and Lumley, J.L. 1972. A first course in turbulence. Cambridge, MA: M.I.T. Press.Google Scholar
  10. 10.
    Golubitsky, M. & Guckenheimer, J. 1986. (eds). Multiparameter Bifurcation Theory. A.M.S. Contemporary Mathematics Series, No. 56. American Mathematical Society, Providence, R.I.zbMATHGoogle Scholar
  11. 11.
    Armbruster, D., Guckenheimer, J. and Holmes, P. 1987. Heteroclinic cycles and modulated traveling waves in systems with 0(2) symmetry. Physica D (to appear).Google Scholar
  12. 12.
    Moffat, H. K. 1989 Fixed points of turbulent dynamical systems and suppression of non-linearity. In Whither Turbulence, ed. J. L. Lumley. Heidelberg: Springer. In press.Google Scholar
  13. 13.
    Lumley, J. L. 1971. Some Comments on the energy method. In Developments in Mechanics 6, eds. L. H. N. Lee and A. H. Szewczyk, pp. 63–88. Notre Dame IN: Notre Dame Press.Google Scholar
  14. 14.
    Kline, S.J., Reynolds, W.C., Schraub, F.A. and Rundstadler, P.W. 1967. The structure of turbulent boundary layers. J. Fluid Mech. 30(4): 741–773.CrossRefGoogle Scholar
  15. 15.
    Corino, E. R., and Brodkey, R.S. 1969. A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37(1):1–30.CrossRefGoogle Scholar
  16. 16.
    Smith, C.R. and Schwarz, S.P. 1983. Observation of streamwise rotation in the near-wall region of a turbulent boundary layer. Phys. Fluids 26(3) 641–652.CrossRefGoogle Scholar
  17. 17.
    Kubo, I. and Lumley, J. L. 1980. A study to assess the potential for using long chain polymers dissolved in water to study turbulence. Annual Report, NASA-Ames Grant No. NSG-2382. Ithaca, NY: Cornell.Google Scholar
  18. 18.
    Lumley, J. L. and Kubo, I. 1984. Turbulent drag reduction by polymer additives: a survey. In The Influence of Polymer Additives on Velocity and Temperature Fields. IUTAM Symposium Essen 1984. Ed. B. Gampert. pp. 3–21. Berlin/Heidelberg: Springer.Google Scholar
  19. 19.
    Aubry, N., Lumley and Holmes, P., J. L. 1989 The effect of drag reduction on the wall region. Submitted to Theoretical and Computational Fluid Dynamics.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • John L. Lumley

There are no affiliations available

Personalised recommendations