Spot concentrations of large-amplitude disturbances in laminar boundary layers.
Quarterly Journal of Mechanics and Applied Mathematics
269 - 281.
A 'spot', in which the amplitudes of linear disturbances are growing exponentially in time, is identified in the low wave-number regime of high-Reynolds-number flow over a surface imperfection. The limiting shape of the spot, which moves downstream with the speed of the fluid at the critical layer, is independent of the initial conditions and is determined by a steepest-descent argument. Comparisons are made between the predictions of the theory and a numerical study of a representative example. Comments, in conclusion, address the relation of this spot to one previously studied in which high oscillatory, but bounded, disturbances are concentrated in the neighbourhood of the bounding caustic.
|Title:||Spot concentrations of large-amplitude disturbances in laminar boundary layers|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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