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Formation of solitons in transitional boundary layers: theory and experiment

Published online by Cambridge University Press:  26 April 2006

Y. S. Kachanov ,
O. S. Ryzhov  and
F. T. Smith
Y. S. Kachanov
Affiliation:
Institute of Theoretical & Applied Mechanics, Novosibirsk, 630090, CIS
O. S. Ryzhov
Affiliation:
Computing Center of Academy of Sciences, Moscow, 117333, Vavilova 40, CIS
F. T. Smith
Affiliation:
Mathematics Department, University College, Gower St, London WC1E 6BT, UK
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Abstract

This work brings together experimental and theoretical studies of nonlinear stages aimed at the K-regime in boundary-layer transition, and some combined theoretical and experimental results are discussed. It is shown that the initial stages in the formation of so-called spikes, observed in many experiments, may be described very well by the asymptotic theory. These flashes-spikes are shown to be (in certain regimes) possible solitons of the boundary layer and governed by the integral-differential Benjamin-Ono equation. Properties of the spike-solitons, obtained both theoretically and experimentally in the quasi-planar stages of their development, are presented. Features of the disturbance behaviour connected with the subsequent development of three-dimensionality are also discussed, as are the effects of viscosity and shorter lengthscales. The main conclusion of the work concerns the hypothesis of the possible soliton nature of the flashes-spikes (within limits), which seems reliably corroborated by the good agreement found between the theory and the experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993 , pp. 273 - 297
Copyright
© 1993 Cambridge University Press

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