Mixed mode transition in boundary layers: Helical instability

Laminar to turbulence transition in attached subsonic boundary layers underneath free stream turbulence is known to proceed via the orderly or bypass routes. In a previous work (Bose & Durbin, Phys. Rev. Fluids, 1, 073602, 2016), an intermediate mixed mode transition regime was reported at super-critical Reynolds numbers. In this regime, the amplitudes of the Klebanoff streaks and instability waves are similar, and these can potentially interact. Mixed mode transition was reported for both zero- and adverse-pressure-gradient boundary layers beneath moderate levels of free stream turbulence (Tu ≤ 2%). Direct Numerical Simulation (DNS) results revealed a secondary streak instability different from the sinuous and varicose forms seen in pure bypass transition. Three-dimensional visualization of the perturbation fields resembled a helical pattern. In the current work, stability analyses are performed for base flow profiles extracted from DNS of mixed mode transition. A helical breakdown is tracked back in time, and cross-stream planes are extracted for the stability analysis. Instability modes are extracted by Arnoldi iterations: they confirm the helical instability, and show how it is quite distinct from previous analyses of streak instability. The mixed mode precursor is the distinctive cause. The phase speed, growth rate and mode shape of the unstable modes are in good agreement with those extracted from the direct simulations. The three-dimensional view of the eigenfunction indeed reveal a helical pattern that is significantly different from the sinous and varicose modes. Based on its phase speed, the helical mode is an inner instability. The streak configuration leading to the formation of the helical instability is different from those leading to the genesis of sinuous and varicose streak instabilities.