A DYNAMICAL-SYSTEMS APPROACH TO THE EARLY STAGES OF BOUNDARY-LAYER-TRANSITION

A series of experiments has been performed on a laminar flat-plate bou ndary layer undergoing transition to turbulence. Reproducible disturba nces were introduced via a loudspeaker embedded at some upstream locat ion. Time series of the velocity fluctuations were obtained at a seque nce of downstream locations using, hot-wire anemometry and the phase p ortraits 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 on to the portrait at the neighbouring downstream position. In this way t he spatial evolution of disturbances is modelled explicitly. These map s agree with classical linear stability theory for small disturbances, and appear to give rise to 'Smale horse-shoe'-like behaviour for larg er amplitude disturbances. This may provide a mechanism for generating sensitive dependence on initial conditions, and illustrates a possibl e role for low-dimensional chaos in boundary-layer transition.