Edge tracking in spatially developing boundary layer flows

TL;DR

This paper extends the concept of the edge manifold to spatially developing boundary layer flows, demonstrating long-time edge tracking and revealing streak switching and coexistence of TS waves, thus offering new insights into boundary layer transition mechanisms.

Contribution

It adapts the edge concept to spatially developing boundary layers and introduces a moving box technique for long-time edge trajectory tracking.

Findings

Edge trajectories exhibit streak switching in the boundary layer.

TS waves coexist with edge structures at long times.

The edge acts as a dividing manifold between bypass and classical transition.

Abstract

Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien--Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.