Transition of Planar Couette Flow at infinite Reynolds numbers

TL;DR

This paper investigates the behavior of planar Couette flow at very high Reynolds numbers, revealing how certain vortex states approach laminar flow and may trigger turbulence.

Contribution

It demonstrates that the Hairpin Vortex State approaches laminar flow as Re increases and may serve as a criterion for transition to turbulence at infinite Re.

Findings

Lower branch of HVS asymptotically approaches laminar state

HVS at high Re belongs to the stability boundary for transition

Unstable manifolds of HVS lie on the transition boundary

Abstract

An outline of the state space of planar Couette flow at high Reynolds numbers ($Re < 10^5$) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of {\it Hairpin Vortex State} (HVS) asymptotically approaches the primary (laminar) state with increasing $Re$. It is also predicted that the lower branch of HVS at high $Re$ belongs to the stability boundary that initiates transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite $Re$ limit.