Heteroclinic connections in plane Couette flow

TL;DR

This paper investigates the complex invariant structures in plane Couette flow, revealing heteroclinic connections that help explain the transition to turbulence despite linear stability of the laminar state.

Contribution

It introduces a numerical method for locating heteroclinic connections between invariant sets in plane Couette flow, advancing understanding of transitional turbulence.

Findings

Heteroclinic connections link invariant solutions in flow dynamics.

Streaks and streamwise rolls change significantly along these connections.

The method aids in understanding the global structure of transitional flow.

Abstract

Plane Couette flow transitions to turbulence for 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 quite distinct from the laminar solution. This article reports several heteroclinic connections between such objects and briefly describes a numerical method for locating heteroclinic connections. Computing such connections is essential for understanding the global dynamics of spatially localized structures that occur in transitional plane Couette flow. We show that the nature of streaks and streamwise rolls can change significantly along a heteroclinic connection.