Existence and Stability of Finite-Amplitude States in Plane Couette Flow
To elucidate the transition mechanism in plane Couette flow we compute finite-amplitude equilibrium solutions by extending numerically 2D nonlinear waves in plane Poiseuille flow to the plane Couette flow limit. The 2D nonlinear states in plane Couette flow take the form of spatially localized (solitarylike) stationary waves, they represent a new basic state for a secondary stability analysis. Secondary stability characteristics are computed as well as secondary bifurcation branches leading to 3D nonlinear states spatially localized in the streamwise direction and periodic in the spanwise direction.
KeywordsStreamwise Direction Spanwise Direction Nonlinear State Equilibrium Surface Secondary Instability
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