The effect of wavepacket frequency bandwidth on the laminar-turbulent transition process in a Blasius boundary layer

Abstract

The subharmonic mode is known to play an important role in a regime of boundary layer transition known as the N (Novosibirsk) or H (Herbert) type. However, until recently, an explanation for its mechanism of production from an input pulse disturbance was lacking. While it is well-known that the subharmonic mode can be amplified by triad resonance interactions, this resonance process is only able to amplify a mode that is already present, but does not show how the mode was initiated or seeded even when it was not present in the initial disturbance pulse. Subsequent researchers have proposed that nonlinear self-interaction among component modes of a wavepacket can generate the subharmonic wave in a wavepacket evolving in a low-speed Blasius boundary layer flow. This hypothesis was tested and verified in experiments, but to date little numerical work had been done. This paper aims to fill in this gap by performing direct numerical simulations (DNS) to gain a better understanding of the process of subharmonic mode generation. The theory predicts the development of the subharmonic to be contingent on the frequency bandwidth of the input disturbance. Indeed, it was found that wide bandwidth signals caused the wavepacket to transition to turbulence via the subharmonic route, whereas narrow bandwidth led to transition through Klebanoff modes (streaks). An interesting hybrid transition scenario was also investigated, in which an intermediate bandwidth input gave rise to wavepacket evolution displaying features of both Klebanoff and subharmonic transition regimes. Furthermore, in any particular transition regime, traces of the other transition mechanisms were uncovered, suggesting that there is competition among the various mechanisms, with the frequency bandwidth being an important factor in determining the path to transition.