Edge states for the turbulence transition in the asymptotic suction boundary layer

TL;DR

This paper identifies an exact invariant solution in the Navier-Stokes equations for the asymptotic suction boundary layer, revealing its role as a local attractor near the laminar-turbulent boundary and its connection to bifurcations in shear flows.

Contribution

It uncovers a long-period periodic orbit as a local attractor in boundary layer flow, linked to bifurcations between laminar and turbulent states, and details its physical and dynamical properties.

Findings

The periodic orbit exists as a local attractor near the stability boundary.

It emerges via a SNIPER bifurcation from plane Couette flow solutions.

The orbit is structurally stable across various Reynolds numbers and domain sizes.

Abstract

We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer we demonstrate that the periodic orbit emerges in a saddle-node infinite-period (SNIPER) bifurcation of two symmetry-related travelling wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size.