Abstract
The problem of the finite-amplitude stability of an incompressible fluid flowing in a channel with compliant walls is studied by numerically calculating the traveling wave solutions that bifurcate from plane Poiseuille flow along a neutral stability curve in the Reynolds number, wave-number plane. This curve is the zero-amplitude intersection of a neutral stability surface in amplitude, Reynolds number, and wave-number space. To determine the differences between the rigid and compliant wall flow, solutions are generated for several compliant wall models. For sufficiently compliant walls the finite-amplitude solutions are stable to two-dimensional periodic disturbances in the limit of small amplitude. However, the solutions destabilize as the amplitude increases. Since these stable solutions exist for such a small range of energy and Reynolds number, these calculations indicate that the process of transition for compliant boundaries is (at least for small amplitude) qualitatively the same as that for rigid boundaries.
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