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Stability of Nonparallel Periodic Flow with Bottom Friction

  • Y. Murakami
  • H. Fukuta
  • K. Gotoh
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

Both linear and nonlinear stabilities of a nonparallel periodic flow:ψ = cos y + A cos x, (0 < A < 1) with bottom-friction effect are investigated numerically. We adopt a quasi-two-dimensional (Q2D) approximation which regards the effect of the boundary layer in a vertical direction as a linear damping term proportional to the horizontal velocity in the two-dimensional (2D) Navier-Stokes equation. The linear critical Reynolds number R Lc (λ, A) increases almost linearly as the bottom-friction effect λ increases. R Lc (λ, A) takes the maximum value at A = 1 for any given λ though the energy density of the main flow is an increasing function of A. The nonlinear critical Reynolds number REc(λ, A) by the energy method is an increasing function of λ while it is a decreasing function of A.

Keywords

Secondary Flow Periodic Flow Nonlinear Stability Energy Method Critical Reynolds Number 
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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Copyright information

© Springer-Verlag, Berlin Heidelberg 1994

Authors and Affiliations

  • Y. Murakami
    • 1
  • H. Fukuta
    • 1
  • K. Gotoh
    • 1
  1. 1.University of Osaka PrefectureSakai 593Japan

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