On shear-layer instability, breakdown and transition

Abstract

The problem of the linear stability of a time-dependent shear flow is investigated and the effects of contraction and expansion of the layer are discussed. Models of flows observed prior to breakdown are constructed and used to investigate the resulting secondary instabilities which are shown to be extremely violent and in essential agreement with recent experiments. In relatively short time, one half period of the primary oscillation, the energy in the secondary disturbance increases by two orders of magnitude; the wave-number corresponding to maximum amplification is five times that of the primary wave.