The late stages of transition induced by a low-amplitude wavepacket in a laminar boundary layer

Abstract

The evolution of a wavepacket in a laminar boundary layer is studied experimentally, paying particular attention to the stage just prior to the formation of a turbulent spot. The initial stages of development are found to be in very good agreement with previous results and indicate a stage in which the disturbance grows according to linear theory followed by a weakly nonlinear stage in which the subharmonic grows, apparently through a parametric resonance mechanism. In a third stage, strong non-linear interactions are observed in which the disturbance develops a streaky structure and the corresponding wavenumber–frequency spectra exhibit an organized cascade mechanism in which spectral peaks appear with increasing spanwise wavenumber and with frequencies which alternate between zero and the subharmonic frequency. Higher harmonics are also observed, although with lower amplitude than the low-frequency peaks. The final (breakdown) stage is characterized by the appearance of high-frequency oscillations with random phase, located at low-speed ‘spike’ regions of the primary disturbance. Wavelet transforms are used to analyse the structure of both coherent and random small-scale structure of the disturbance. In particular, the breakdown oscillations are also observed to have a wavepacket character riding on the large-amplitude primary disturbance.