Heteroclinic connections in plane Couette flow

Abstract

Plane Couette flow transitions to turbulence at Re ≈ 325 even though the laminar solution with a linear profile is linearly stable for all Re (Reynolds number). One starting point for understanding this subcritical transition is the existence of invariant sets in the state space of the Navier–Stokes equation, such as upper and lower branch equilibria and periodic and relative periodic solutions, that are distinct from the laminar solution. This article reports several heteroclinic connections between such objects and briefly describes a numerical method for locating heteroclinic connections. We show that the nature of streaks and streamwise rolls can change significantly along a heteroclinic connection.