The Combined Effects of Wavepacket Frequency, Amplitude and Bandwidth on its Transition Process in a Boundary Layer

Direct numerical simulations (DNS) were used to investigate the effect of frequency bandwidth on the laminar-turbulent transition of wavepackets evolving in a Blasius boundary layer under a total of 18 different combinations of wavepacket frequency, amplitude and bandwidth. Extensive comparisons with linear stability theory (LST) were also performed with a program written to automat- ically calculate the spatial amplification of an ensemble of modes in a wavepacket, enabling the linear and nonlinear aspects of the wavepacket development to be clearly distinguished. Input disturbances that are wide in terms of frequency bandwidth encouraged N-type (Novosibirsk) transition, while narrow-bandwidth disturbances favoured K-type (Klebanoff) transition. However, the initial amplitude and frequency composition of the wavepacket also play an important role in the transition process, with higher-amplitude initial disturbances leading to an increased number of K-type transition events, while frequency compositions that are dominated by linearly damped or slow-growing modes are more likely to transition via the N-route. Moreover, there is a certain preferred frequency of the wavepacket, corresponding to the lower branch point on the neutral stability curve at the disturbance source. The transition process appeared to be most sensitive to changes in bandwidth when the wavepacket is dominated by its preferred frequency.