Laminar-turbulent boundary in plane Couette flow

TL;DR

This study uses an iterative algorithm to identify the boundary between laminar and turbulent states in plane Couette flow at Re=400, revealing the structure of the edge state and its stability properties.

Contribution

It demonstrates that the iterated edge state tracking algorithm reliably finds the laminar-turbulent boundary and the associated edge state in plane Couette flow.

Findings

Edge state is a hyperbolic coherent structure in state space.

Algorithm converges to the edge state regardless of initial conditions.

Edge state has only one unstable direction in the studied case.

Abstract

We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent nor weak enough to relaminarize tend towards a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, as for the lower branch solution in in plane Couette flow, the iterated edge tracking algorithm converges to this state. They also show that choice of initial state is not critical, and that essentially arbitrary initial conditions can be used to find the edge state.