Stability of Nonparallel Periodic Flow with Bottom Friction
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.
KeywordsSecondary Flow Periodic Flow Nonlinear Stability Energy Method Critical Reynolds Number
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