Streak instabilities in boundary layers beneath free-stream turbulence

Abstract

AbstractThe secondary instability of boundary layer streaks is investigated by means of direct stability analysis. The base flow is computed in direct simulations of bypass transition. The random nature of the free-stream perturbations causes the formation of a spectrum of streaks inside the boundary layer, with breakdown to turbulence initiated by the amplification of localized instabilities of individual streaks. The capability of the instability analysis to predict the instabilities which are observed in the direct numerical simulation is established. Furthermore, the analysis is shown to identify the particular streaks that break down to turbulence farther downstream. Two particular configurations of streaks regularly induce the growth of these localized instabilities: low-speed streaks that are lifted towards the edge of the boundary layer, and the local overlap between high-speed and low-speed streaks inside the boundary layer. It is established that the underlying modes can be ascribed to the general classification of inner and outer modes which was introduced by Vaughan & Zaki (J. Fluid Mech., vol. 681, 2011, pp. 116–153). Statistical evaluations show that Blasius boundary layers favour the amplification of outer instabilities. Adverse pressure gradient promotes breakdown to turbulence via the inner mode.