Nonlinear Stability of Kolmogorov Flow with Bottom-Friction Using the Energy Method
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概要
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Stability of Kolmogorov flow : U= -sin y to any finite disturbances is treated by using the energy method. The linear damping term - λu due to the bottom friction is taken into account. The Euler-Lagrange equation is solved numerically and analytically to determine the critical Reynolds number, R_<Ec>, below which subcritical instability cannot occur. It is shown numerically that R_<Ec> and the linear critical Reynolds number, R_<LC> are of the same order in 0 < λ < 200. The critical wavenumber, (α_<Ec>, β_<Ec>)is always (0, 0) when λ<49. 1 ; otherwise α_<Ec>≠ 0. By using a small wavenumber expansion, it is obtained that R_E=[8λ(λ+1)]^<1/2> at α=0. In the limit λ→∞, numerical results suggest that R_<Ec>→2λ and α_<Ec>→∞. In this limit for general parallel flow U(y)the relation : (2/M)λ<R_<Ec><R_<Lc>=(1/σ_0)λ is obtained analytically where M=max_y |∂U/∂y|, and σ_0 is the inviscid maximum growth rate.
- 社団法人日本物理学会の論文
- 1995-10-15
著者
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MURAKAMI Youichi
Department of Physics, Tohoku University
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Murakami Youichi
Department Of Aerospace Engineering College Of Engineering University Of Osaka Prefecture
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Murakami Youichi
Department Of Aerospace Engineering College Of Engineering Osaka Prefecture University
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Fukuta Hiroaki
Department of Mathematical Sciences, College of Engineering, University of Osaka Prefecture
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Fukuta H
Osaka Prefecture Univ. Osaka Jpn
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Fukuta Hiroaki
Department Of Mathematical Sciences College Of Engineering Osaka Prefecture University
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Murakami Youichi
Department of Aerospace Engineering, College of Engineering, University of Osaka Prefecture
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