Edge tracking in spatially developing boundary layer flows

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.

arXiv comment17 pages, 12 figures

References in corpus (5)

• Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?
• Edge states as mediators of bypass transition in boundary-layer flows
• Laminar-turbulent separatrix in a boundary layer flow
• A critical point for bifurcation cascades and featureless turbulence
• Harbingers and latecomers - The order of appearance of exact coherent structures in plane Poiseuille flow

Cited by in corpus (6)

• On the Kármán momentum-integral approach and the Pohlhausen paradox
• A critical point for bifurcation cascades and featureless turbulence
• The edge as a Lagrangian Coherent Structure in a high-dimensional state space
• Optimal perturbations and transition energy thresholds in boundary layer shear flows
• Subcritical transition to turbulence in quasi-two-dimensional shear flows
• A model for the collapse of the edge when two transitions routes compete