Abstract
Linear perturbation analyses of zero-pressure-gradient boundary layers at subcritical Reynolds numbers predict that transient disturbance amplification can take place due to the lift-up mechanism. Upstream, streamwise-elongated vortices yield the largest response per unit of inflow disturbance energy, which takes the form of streamwise-elongated streaks. In this work, we compute the linear and also nonlinear inflow disturbances that generate the largest response inside the boundary layer, for flow over a thin flat plate with a slender leading edge. In order to compare our results with earlier linear analyses, we constrain the inlet disturbance to be monochromatic in time, or a single frequency. The boundary layer effectively filters high frequencies, and only low-frequency perturbations induce a strong response downstream. The low-frequency optimal inflow disturbance has a spanwise wavenumber that scales with $\sqrt{Re}$, and it consists of streamwise and normal vorticity components: the latter is tilted around the leading edge into the streamwise direction and, further downstream, generates streaks. While none of the computed monochromatic disturbances alone can lead to breakdown to turbulence, secondary instability analyses demonstrate that the streaky base state is unstable. Nonlinear simulations where the inflow disturbance is supplemented with additional white noise undergo secondary instability and breakdown to turbulence.
Highlights
Bypass transition refers to the evolution of a boundary-layer flow from laminar to turbulent in response to external forcing with perturbation intensities larger than 0.5 % of the free-stream speed
The secondary instability of the streaky base state was evaluated at various downstream locations in the region from x = 92 to x = 106; the perturbation streaks at these locations are plotted in figure 15
It interacts with the boundary layer starting from the leading edge of the plate, and the response are streaks which are prone to secondary instability
Summary
Bypass transition refers to the evolution of a boundary-layer flow from laminar to turbulent in response to external forcing with perturbation intensities larger than 0.5 % of the free-stream speed. The early stages involve the interaction of the external perturbations with the laminar flow profile – an interaction that gives rise to amplifying velocity streaks. These structures are elongated in the downstream direction, and are dominated by the streamwise velocity perturbation. Zaki spots (e.g. see review by Zaki (2013)) Owing to their role in bypass transition, streaks have been studied extensively using experiments, simulations and linear theory. We consider nonlinear disturbances, but constrain the inlet spectra to be monochromatic in time in order to distinguish the roles of different frequencies within a general broadband free-stream perturbation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
