Mixed mode transition in boundary layers: Helical instability

Recent [Bose and Durbin, Phys. Rev. Fluids 1, 073602 (2016), 10.1103/PhysRevFluids.1.073602] direct numerical simulations (DNS) of adverse- and zero-pressure-gradient boundary layers beneath moderate levels of free stream turbulence (T u ≤2 % ) revealed a mixed mode transition regime, intermediate between orderly and bypass routes. In this regime, the amplitudes of the Klebanoff streaks and instability waves are similar, and both can contribute significantly as these interact. Three-dimensional visualizations of transitional eddies revealed a helical pattern, quite distinct from the sinuous and varicose forms seen in pure bypass transition. This raises the fundamental question of whether the helical pattern could be attributed to a previously unknown instability mode. In the present work, based on stability analyses, we show that it is indeed the case. Two-dimensional stability analyses are performed herein for base flows extracted from DNS flow fields. The three-dimensional structure of the eigenfunction of the most unstable mode indeed reveals a helical pattern. The instability arises well upstream of the appearance of helical structures in flow visualizations. In DNS, fluctuations at wavelengths corresponding to the instability modes have negligible energy in the upstream region. Due to their high growth rates, these instability modes develop into helical patterns in the transition region, which quickly break down. The streak configuration leading to the formation of the helical mode instability is different from those leading to sinuous and varicose modes, analyzed in previous studies of pure bypass transition. Thus, the mixed mode precursor is the distinctive cause of helical mode transition.