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

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 numeri...

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Bibliographic Details
Published in:Journal of fluid mechanics 1988-09, Vol.194 (1), p.295-307
Main Authors: Pugh, J. D., Saffman, P. G.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Physics
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S002211208800299X