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The Spanwise Confined One-Stream Mixing Layer

  • D. Hilberg
  • H. E. Fiedler
Conference paper

Abstract

In many technical or geophysical flows we find turbulent shear layers with notably larger lateral extent H than spanwise width B, being bounded either by walls or by open surfaces. A typical example is the plane jet in shallow water, as e.g. in river estuaries (Giger [l]). Below a critical ratio B/H (or B/L) the behaviour of the turbulent shear layer is found to be markedly different from its usual appearance, forming distinct structures of large scale and strong periodicity. The phenomenon is demonstrated by a juxtaposition of three smoke pictures shown in fig. 1. We observe
  1. (a)

    the regular - “wide” - mixing layer (B/L = 0.25, uo = 8 m/s)

     
  2. (b)

    same geometric conditions - periodically excited (uo = 11 m/s), and

     
  3. (c)

    the “narrow” layer: natural periodicity (B/L = 0.016, uo = 4 m/s)

     
where the third case shows a quality different from the other two: Apart from global and superficial similarity we observe a distinctly random character in (a), a prominent structural periodicity in (b) with, however, non-linear overall growth and longitudinal development of growth and decay of the vortical structures (Fiedler & Mensing [2]). The situation in (c) is characterized by what appears to be a full-cycle periodic wave of strong amplitude, chracteristic for a resonant system. In this case the visible spread is approximately 50% larger than in (a). This then seems to be a case of general interest for a number of reasons, e.g.:
  • it provides a model situation for constrained shear flows as found in nature, e.g. in civil engineering applications and in meteorology.

  • it is of general interest in view of the possibility of controlling turbulent flows via stationary boundary conditions

  • it may provide a case of study for a situation with absolute instability

  • it may also provide a case for low dimensional chaos.

Keywords

Shear Layer Horseshoe Vortex Absolute Instability Downstream Position Stationary Boundary Condition 
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.

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References

  1. [1]
    M. Giger, Der ebene Freistrahl in flachem Wasser. Doctoral thesis, ETH Zrich, 1987Google Scholar
  2. [2]
    H. Fiedler and P. Mensing, The plane turbulent shear layer with periodic excitation. J. Fluid Mech., 150, pp. 281–309, 1985CrossRefADSGoogle Scholar
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    Cohen and I. Wygnanski, The evolution of instabilties in the axisymmetric jet. Part 2. The flow resulting from interaction between two waves, J. Fluid Mech., 176, pp. 221–235, 1987CrossRefADSGoogle Scholar
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    P. Huerre and P. Monkewitz, Absolute and convective instabilities in free shear layers, J. Fluid Mech., 159, pp. 151–168, 1985CrossRefMATHADSMathSciNetGoogle Scholar
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    C.-M. Ho, Local and global dynamics of free shear layers, Proceedings of Symposium on Numerical and Physical Aspects of Aerodynamic Fows, Long Beach, Ca., January 1981Google Scholar
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    Lasheras, J. C. and Maxworthy, T. Structure of the Vorticity Field in a Plane Free Shear-Layer, Turbulent Shear Flows 5 (ed. Durst, Launder, Schmid t, Whitelaw), Springer Verlag, pp. 124–133, 1987CrossRefGoogle Scholar
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    Bernal, L.P. and Roshko, A., Streamwise vortex structure in plane mixing layers, J.F.M., 170, pp. 499–525, 1986CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • D. Hilberg
    • 1
  • H. E. Fiedler
    • 1
  1. 1.Hermann-Föttinger-Institut für Thermo- und FluiddynamikTU BerlinBerlinGermany

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