Subcritical finite-amplitude solutions in plane Couette flow of visco-elastic fluids

TL;DR

This paper demonstrates that visco-elastic fluids in plane Couette flow can exhibit a purely elastic subcritical instability, leading to secondary flows at finite perturbation amplitudes, with implications for understanding weak turbulence.

Contribution

It provides the first nonlinear stability analysis showing subcritical elastic instability in visco-elastic plane Couette flow and characterizes the critical conditions for secondary flow onset.

Findings

Instability occurs above a critical Weissenberg number.

Small finite perturbations can trigger secondary flows.

Threshold perturbation amplitude decreases with increasing Weissenberg number.

Abstract

Plane Couette flow of visco-elastic fluids is shown to exhibit a purely elastic subcritical instability in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. It is found that above the critical Weissenberg number, a small finite-size perturbation is sufficient to create a secondary flow, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases. The results suggest a scenario for weakly turbulent visco-elastic flow which is similar to the one for Newtonian fluids as a function of Reynolds number.