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)


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.


Secondary Flow Periodic Flow Nonlinear Stability Energy Method Critical Reynolds Number 
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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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