A theoretical model of a wave packet in the boundary layer on a flat plate

Abstract
A linear model of a wave packet in a laminar boundary layer is proposed. The model wave packet was chosen to conform to a particular experimental situation where a packet was artificially excited by a localized pulsed perturbation at the wall boundary. Appropriate quantities were computed from this model and these have been compared directly with experimental measurements. The model disturbance was built up from a linear combination of spatially growing modes summed numerically over all wavenumbers and frequencies. The input spectrum was assumed to be flat (all modes were equally excited), and the downstream development of the frequency-wavenumber spectrum was calculated on the basis of linear stability theory. The development of the model wave packet was compared with that of the experiment. It was found that the overall shapes of the disturbed region and the way it spread out as the packet travelled downstream were well predicted by the model behaviour. Detailed comparisons of the wave motion within the wave packet were also made and although encouraging correlation was achieved at stations close to the source this was not maintained far downstream where the experimental packet showed various irregularities. The wave packet generated by the summation of modes developed smoothly downstream without forming any of the types of distortions which had been observed in the experiment.

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