Nonlinear Instability of Nonparallel Flows pp 320-329 | Cite as

# Stability of Nonparallel Periodic Flow with Bottom Friction

## Abstract

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 R_{Ec}(λ, *A*) by the energy method is an increasing function of λ while it is a decreasing function of *A*.

## Keywords

Secondary Flow Periodic Flow Nonlinear Stability Energy Method Critical Reynolds Number## Preview

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