抄録
Stability of Kolmogorov flow: U=-sin y to any finite disturbances is treated by using the energy method. The linear damping term -λ u due to the bottom friction is taken into account. The Euler-Lagrange equation is solved numerically and analytically to determine the critical Reynolds number, REc, below which subcritical instability cannot occur. It is shown numerically that REc and the linear critical Reynolds number, RLc are of the same order in 0<λ <200. The critical wavenumber, (αEc, , βEc) is always (0, , 0) when λ <49.1; otherwise α Ec≠ 0. By using a small wavenumber expansion, it is obtained that RE= [8λ (λ +1)]1/2 at α=0. In the limit λ → ∞, numerical results suggest that REc→ 2λ and αEc→ ∞. In this limit for general parallel flow U(y) the relation: (2/M)λ EcLc=(1/σ0)λ is obtained analytically where M=maxy, | ∂ U/∂ y|, and σ0 is the inviscid maximum growth rate.
