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A dynamical systems approach to the early stages of boundary-layer transition

Published online by Cambridge University Press:  26 April 2006

J. J. Healey
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Abstract

A series of experiments has been performed on a laminar flat-plate boundary layer undergoing transition to turbulence. Reproducible disturbances were introduced via a loudspeaker embedded at some upstream location. Time series of the velocity fluctuations were obtained at a sequence of downstream locations using hot-wire anemometry and the phase portraits were reconstructed at each position. A new technique has been used to estimate the number of independent modes. Nonlinear maps were then fitted that transform the portrait at one streamwise location onto the portrait at the neighbouring downstream position. In this way the spatial evolution of disturbances is modelled explicitly. These maps agree with classical linear stability theory for small disturbances, and appear to give rise to ‘Smale horse-shoe’-like behaviour for larger amplitude disturbances. This may provide a mechanism for generating sensitive dependence on initial conditions, and illustrates a possible role for low-dimensional chaos in boundary-layer transition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 667 - 681
Copyright
© 1993 Cambridge University Press

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