A continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow

TL;DR

This paper demonstrates a novel elastic linear instability in inertialess, rectilinear shear flow of ultra-dilute polymer solutions, revealing a continuous transition pathway between elastic and elasto-inertial turbulence states.

Contribution

It reports the first purely elastic linear instability in a rectilinear shear flow and links elastic and elasto-inertial turbulence through a continuous pathway.

Findings

Elastic instability occurs at high elasticity in inertialess flow.

A single unstable mode connects elastic and elasto-inertial turbulence.

Transition to turbulence can happen at zero Reynolds number.

Abstract

We show that viscoelastic plane Poiseuille flow becomes linearly unstable in the absence of inertia, in the limit of high elasticities, for ultra-dilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues upto a Reynolds number ($Re$) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultra-dilute polymer solutions, a single linearly unstable modal branch may underlie transition to elastic turbulence at zero $Re$, and to elasto-inertial turbulence at moderate $Re$, implying the existence of continuous pathways connecting the turbulent states to each other, and to the laminar base state.