Mixing layer instability and vorticity amplification in a creeping viscoelastic flow

TL;DR

This study demonstrates elastic instability and vorticity amplification in a creeping viscoelastic flow with high elasticity, revealing new insights into flow stability and turbulence mechanisms at low Reynolds numbers.

Contribution

It provides the first quantitative evidence of mixing-layer elastic instability and vorticity amplification in a viscoelastic flow at low Reynolds number and high Weissenberg number.

Findings

Elastic instability occurs near inflection points in shear velocity profiles.

Vorticity is amplified in the elastic turbulence regime.

Scaling laws for friction factor, pressure, and velocity spectra are established.

Abstract

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at $Re\ll1$ and $Wi\gg1$. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatio-temporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with $Wi$, and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e. $Wi\gg1$ and $Re\ll1$, and oppose the current view of suppression of vorticity solely by polymer additives.