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.
KeywordsVortex Sine Bove
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- Bondarenko, N.F. M.Z.Gak,& F.V.Dolzhanskiy,1979 Laboratory and theoretical models of plane periodic flows, Izv. Atmos. Ocean. Phys., 15, 711–716.Google Scholar
- Dolzhanskiy, F.V. 1987 Effect of external friction on the stability of plane-parallel flows in a homogeneous incompressible liquid, Izv. Atmos. Ocean. Phys., 23, 262–268.Google Scholar
- Matsuda, N. 1993 B.S. in Univ. of Osaka Prefecture, (in Japanese)Google Scholar
- Murakami, Y. & H.Fukuta,1993 Nonlinear stability of the Kolmogorov flow with bottom-friction using the energy method, to appear in Proceedings of Analysis of Nonlinear Phenomena and Its Application RIMS, Kyoto.Google Scholar
- Murakami, Y. II. Fukuta & K.Gotoh,1993 in preparationGoogle Scholar