Zhao Geng-fu, Zhou Heng. Weakly Nonlinear Theory versus Theory of Secondary Instability for Plane Poiseuille Flow[J]. Applied Mathematics and Mechanics, 1988, 9(7): 571-576.
Citation: Zhao Geng-fu, Zhou Heng. Weakly Nonlinear Theory versus Theory of Secondary Instability for Plane Poiseuille Flow[J]. Applied Mathematics and Mechanics, 1988, 9(7): 571-576.

Weakly Nonlinear Theory versus Theory of Secondary Instability for Plane Poiseuille Flow

  • Received Date: 1987-05-10
  • Publish Date: 1988-07-15
  • In [1] the theory of secondary instability for plane Poiseuille flow was proposed. In this paper the weakly nonlinear theory is used to investigate the same problem. The results are consistent with those of the theorv of secondary instability. It indicates that for plane Poiseuille flow there exists a certain intrinsic relation between the weakly nonlinear theory and the theory of secondary instability.
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  • [1]
    Herbert, T., Subharmonic Three-Dimensional Disturbances in Unstable Plane Poiseuille Flow. s, AIAA-83-1759, (1983).
    [2]
    Klebanoff, P.S., K.D. Tidstrom & L.M. Sargent,Three-Dimensional Nature of BoundaryLayer Instability, J. Fluid Mech, 12 (1962), 1-34.
    [3]
    Nishioka. M., M. Asai. & S. Ⅱda, Laminar-Turbulent Transition. (eds. R. Eppler & H. Fasel). Springer-Verlag (1980), 37-46.
    [4]
    Benney. D.T. & C.C. Lin, On the Secondary Motion Induced by Oscillationsina Shear How. Phy. Fluids, 3 (1960), 656-657.
    [5]
    Craik, A.D.D., Non-linear Resonant Instability in Boundary Layers. J. Fluid Mech. 50(1971). 393-413.
    [6]
    周恒,力学学报,16(1984),1-9.
    [7]
    周恒,王亦工,力学学报,16(1984), 205-213.
    [8]
    Orszag S.A. & A.T. Patera. Secondary Instability of Wall-Bounded Shear Hows. J. Fhuid Mech., 128 (1983), 347-383.
    [9]
    Nishioka, M.and M. Asai, Second IUTAM Svmpoimn on I aminar-Turbulent Transition. Novosibirsk. (July. 1984).
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