Two-dimensional superharmonic stability of finite-amplitude waves in plane Poiseuille flow

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Abstract
In recent work on shear-flow instability, the tacit assumption has been made that the two-dimensional stability of finite-amplitudes waves in plane Poiseuille flow follows a simple and well-understood pattern, namely one with a stability transition at the limit point in Reynolds number. Using numerical stability calculations we show that the application of heuristic arguments in support of this assumption has been in error, and that a much richer picture of bifurcations to quasi-periodic flows can arise from considering the two-dimensional superharmonic stability of such a shear flow.

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