Low Dimensional Models, Wavelet Transforms and Control

  • N. Aubry
  • G. Berkooz
  • B. Coller
  • J. Elezgaray
  • P. Holmes
  • J. L. Lumley
  • A. Poje
Part of the International Centre for Mechanical Sciences book series (CISM, volume 353)


If we examine pictures of various turbulent flows, we will discover that the proportion of organized and disorganized turbulence in each flow is different. For example, if we look at mixing layers from undisturbed initial conditions (with only thin laminar boundary layers on the splitter plate), we find that there is an energetically large organized component, which only relatively slowly becomes three-dimensional and disorganized, although the nearly two-dimensional organized structures have from the beginning a stochastic component, so that their occurrence is not precisely periodic, nor are their strengths equal. On the other hand, if we examine a mixing layer from quite disturbed initial conditions, with a thick, turbulent boundary layer on the splitter plate, we find that the proportion of organized component is considerably less — although the organized component is still visible, it is no longer dominant. Thus, in the same type of flow, we find that the initial conditions change the relative strength of the organized and disorganized components. We we examine a different flow, for example a jet, we find the same difference — that is, if the flow from the orifice is initially undisturbed — thin laminar boundary layers on the inner surface of the nozzle — then there is initially a laminar instability which gradually becomes three-dimensional and undergoes transition, leaving in the downstream development of the turbulence the remnants of the instability structure. On the other hand, if the boundary layers on the inside of the nozzle are initially thick and turbulent, there is no initial laminar instability, and there are no visible organized remnants in the turbulent motion. More than this, however, there is evidently a substantial difference between this flow and the mixing layer. Even in the undisturbed state, the organized component of this flow is a very great deal weaker than that in the mixing layer under the same circumstances. It is bearly discernible; when the initial conditions are disturbed, the organized structure becomes essentially undetectable. Thus, we can conclude that different flows, even under similar conditions, have different relative strengths of organized and disorganized components.


Large Eddy Simulation Reynolds Stress Turbulent Boundary Layer Coherent Structure Proper Orthogonal Decomposition 
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Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • N. Aubry
    • 1
  • G. Berkooz
    • 1
  • B. Coller
    • 1
  • J. Elezgaray
    • 1
  • P. Holmes
    • 1
  • J. L. Lumley
    • 1
  • A. Poje
    • 1
  1. 1.Cornell UniversityIthacaUSA

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