An Alternative Approach to Disturbances in Boundary Layers

  • P. F. Easthope
  • W. O. Criminale

Abstract

By modelling the boundary layer on a flat plate as a piece-wise linear velocity profile it is possible to analyze disturbances in the flow in a systematic manner. The approach is that of an initial-value, boundary-value problem but, unlike classical normal modes employed in stability theory, the solutions here can be obtained in closed form and they are non separable. A specific example is treated where the vertical component of the perturbation velocity is prescribed as a localized pulse initially. The amplitude is then depicted as a function of time and the coordinates of the plane of the flat plate at a fixed vertical location. The role of three-dimensionality and the initial transient period of development — heretofore unknown — are both shown to be of significant importance in the dynamics. An argument is given to strongly suggest that the origin of large-scale oscillations known to be prevelant in turbulent shear flows may well be explained using these bases.

Keywords

Vorticity Smoke Hunt 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Betchov, R., Criminale, W.O., 1967, Stability of Parallel Flows, Academic Press.Google Scholar
  2. [2]
    Criminale, W.O. and Kovasznay, L.S.G., 1962, The growth of localized disturbances in a laminar boundary layer, J. Fluid Mech.1459–80.MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    Criminale, W.O., 1987, Understanding the origins of coherent structure, Proceedings, 2nd Inth. Symp. on Transport Phenomena in Turbulent Flows, Tokyo.Google Scholar
  4. [4]
    Criminale, W.O. and Drazin, P.G., 1990. The evolution of linearized perturbations of parallel flows, Stud. Appl. Math.83: 2, 123–157.MathSciNetGoogle Scholar
  5. [5]
    Drazin, P.G., Reid, V.H., 1981, Hydrodynamic Stability, Cambridge Univ. Press.MATHGoogle Scholar
  6. [6]
    Easthope, P.F., 1984, An alternative approach to layer disturbances, Ph.D. Diss., University of WashingtonGoogle Scholar
  7. [7]
    Gaster, M. and Grant, I. 1975, An experimental investigation of the formation and development of a wave-packet in a boundary layer, Proc. Roy. Soc. London A347, 253–269.ADSCrossRefGoogle Scholar
  8. [8]
    Gaster, M., 1975, A theoretical model of a wave packet in the boundary layer on a flat plate, Proc. Roy. Soc. London A347, 271–289.ADSCrossRefGoogle Scholar
  9. [9]
    Gustavsson, L.H., 1979, Initial value problem for boundary layer flows, Phys. Fluids, 22(9): 1602–1605.MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    Gustavsson, C.H. and Hultgren, L.S., 1980, A resonance mechanism in plane couette flow, J. Fluid Mech., 98, 149–159.MathSciNetADSMATHCrossRefGoogle Scholar
  11. [11]
    Klebanoff, P.S., Tidstrom, K.D., and Sargent, L.M., 1962, The three dimensional nature of boundary layer instability, J. Fluid Mech., 12, 1–34.ADSMATHCrossRefGoogle Scholar
  12. [12]
    Landahl, M.T., 1980, A note on an algebraic instability of inviscid parallel shear flows, J. Fluid Mech., 98, 243–251.MathSciNetADSMATHCrossRefGoogle Scholar
  13. [13]
    Lee, M.J., Hunt, J.C.R., 1990, The Structures of sheared turbulence near a plane boundary, Turbulent Shear Flows, 7: 1–20, Springer Verlag.Google Scholar
  14. [14]
    Lin, C.C., 1955, The Theory of Ilydrodynamic Stability, Cambridge Univ. Press.MATHGoogle Scholar
  15. [15]
    Mack, L.M., 1976, A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech.73, 497–520.ADSMATHCrossRefGoogle Scholar
  16. [16]
    Townsend, A.A., 1976, The Structure of Turbulent Shear Flow, Cambridge Univ. Press.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • P. F. Easthope
    • 1
  • W. O. Criminale
    • 1
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

Personalised recommendations