Resemblance of K- and N-regimes of boundary-layer transition at late stages

Abstract

This paper is devoted to an experimental study of late nonlinear stages of laminar–turbulent transition in a 2D flow close to the Blasius boundary-layer. The measurements were conducted at controlled disturbance conditions with excitation of a 2D large-amplitude fundamental instability wave with frequency f 1 and/or a pair of low-amplitude oblique subharmonic instability waves with frequency f 1/2 and values of the spanwise wavenumber ± β 1/2 . In the case with a phase shift between the fundamental mode and the pair of the subharmonics favourable for the subharmonic resonance the transition process was found to be characterised by a rapid resonance growth of the 3D subharmonic modes. This was followed by a formation of the Λ-structures within each subharmonic period in time, positioned in a staggered order in space that is typical of the N-regime (or the subharmonic regime) of the boundary layer breakdown. However, at late stages of the disturbance development the local behaviour of the perturbations in the vicinity of the Λ-structures turned out to be very similar to that typically observed in the K-regime of breakdown. This could be seen in the formation of an intensive Λ-shaped 3D high-shear layer and the coherent structures associated with spikes in the time-traces of the hot-wire signal. Sets of consecutive spikes were found to be generated in the vicinity of the tip of each Λ-structure. The arrays of spikes had also the staggered order with the streamwise and spanwise spacing characteristic of the subharmonic wave (as in the N-regime) but their local properties were found to be qualitatively the same as those typical for the K-regime. Despite the significantly different nature of the initial stages of these two scenarios of transition, described usually in terms of weakly nonlinear interactions of the instability waves, the late stages of these two types of breakdown (described usually in terms of vortices attributed to the coherent structures) have approximately the same physical nature.