Abstract
The disturbing motion of plane Couette and Poiseuille flow is described using three parameters: two amplitudes corresponding to the disturbance of the parallel flow and the cellular motion, respectively, and the angle ϕ0 which defines the orientation of the vortex blobs with respect to the parallel flow. Equations of motion for these parameters are obtained using a Ritz-Galerkin method. For Reynolds numbers above a critical value sufficiently big disturbances will grow until a steady finite amplitude state is achieved. The energy of the disturbance remains finite, in spite of the highly truncated field representation using only three parameters. This is possible because of the nonlinear dependence of the field functions on ϕ0. The critical values of Reynolds number, above which finite amplitude states exist, are computed for the plane Couette flow and the Poiseuille channel flow.
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