# Elastic wake instabilities in a creeping flow between two obstacles

## TL;DR

This paper investigates elastic wake instabilities in a creeping viscoelastic flow between two obstacles, revealing two elastic bifurcations and a novel vorticity growth mechanism contrary to Newtonian flow behavior.

## Contribution

It identifies two elastically driven bifurcations and uncovers a new vorticity growth mechanism in viscoelastic flow, contrasting with classical Newtonian flow suppression.

## Key findings

- Two elastic bifurcations associated with symmetry breaking.
- Collapse of bifurcations into a codimension-2 point with obstacle proximity.
- Vorticity growth via vortex length increase at preserved streamline curvature.

## Abstract

It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the cylinders. The quantitative characterization of instabilities in a creeping viscoelastic channel flow between two widely spaced cylinders reveals two elastically driven transitions, which are associated with the breaking of time-reversal and mirror symmetries: Hopf and forward bifurcations described by two order parameters $\mbox{v}_{rms}$ and $\bar{\omega}$, respectively. We suggest that a decrease of the normalized distance between the obstacles leads to a collapse of the two bifurcations into a codimension-2 point, a situation general for many non-equilibrium systems. However, the striking and unexpected result is the discovery of a mechanism of the vorticity growth via an increase of a vortex length at the preserved streamline curvature in a viscoelastic flow, which is in sharp contrast to the well-known suppression of the vorticity in a Newtonian flow by polymer additives.