Fluid Dynamics

, Volume 29, Issue 6, pp 765–769 | Cite as

Possibility of describing the nonlinear stage of subharmonic transition within the framework of amplitude equations

  • M. V. Ustinov


In order to determine the limits of applicability of Craik's model, the results of calculations obtained in accordance with this model are compared with the conclusions of the more exact theory of secondary instability proposed by Herbert and the results of direct numerical simulation of laminar-turbulent transition. An analysis of the results obtained shows that Craik's model describes the development of perturbation adequately only up to the amplitudes of the order of 10−3 times the free-stream velocity.


Fluid Dynamics Direct Numerical Simulation Exact Theory Amplitude Equation Secondary Instability 
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  1. 1.
    A. D. Craik, “Nonlinear resonant instability in boundary layers,”J. Fluid Mech.,50, 393 (1971).Google Scholar
  2. 2.
    M. B. Zel'man, “Nonlinear development of perturbations in plane-parallel flows,”Izv. SO Akad. Nauk USSR, Ser. Tekhn. Nauk,3, No. 13, 16 (1974).Google Scholar
  3. 4.
    Yu. S. Kachanov and B. Ya. Levchenko, “Resonance interaction of perturbations in transition to turbulence in a boundary layer,” Preprint No. 10 [in Russian] Institute of Technical and Applied Mechanics, Siberian Branch of the Academy of Sciences of the USSR, Moscow (1982).Google Scholar
  4. 5.
    T. Herbert, “Secondary instability of plane channel flow to subharmonic three-dimensional disturbances,”Phys. Fluids,26, 871 (1983).Google Scholar
  5. 6.
    T. Herbert, “Analysis of the subharmonic route to transition in boundary layer,”AIAA. Pap., No. 0009 (1984).Google Scholar
  6. 7.
    M. V. Ustinov, “Investigation of subharmonic transition in a plane channel by direct numerical simulation,”Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 46 (1993).Google Scholar
  7. 8.
    M. A. Gol'dshtik and V. N. Shtern, Hydrodynamic Stability and Turbulence [in Russian], Nauka, Novosibirsk (1977).Google Scholar
  8. 9.
    B. Singer, H. L. Reed, and J. H. Ferziger, “Investigation of the effects of initial disturbances on plane channel transition,”AIAA Pap., No. 0433 (1986).Google Scholar
  9. 10.
    T. C. Corke and R. A. Mangano, “Resonant growth of three-dimensional modes in transitioning Blasius boundary layers,”J. Fluid Mech.,209, 93 (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • M. V. Ustinov

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