Waves dictate the yo-yoing decay of a viscoelastic mixing layer

TL;DR

This paper reveals that waves in viscoelastic fluid mixing layers cause the mean flow to oscillate, contrasting with Newtonian fluids, and provides a theoretical model predicting this yo-yoing behavior.

Contribution

It uncovers the wave-driven yo-yoing of the mean flow in viscoelastic mixing layers and offers an analytical model explaining the phenomenon.

Findings

Waves develop in viscoelastic mixing layers, causing oscillations in the mean flow.

Theoretical analysis links energy injection by polymers to flow oscillations.

Mathematical solutions predict the period and conditions of yo-yoing.

Abstract

We find that waves develop in a time-decaying mixing layer of viscoelastic fluid, leading the mean-flow to yo-yo. This is in sharp contrast with Newtonian fluids, where laminar mixing layers evolve monotonically. We combine direct numerical simulations with a theoretical analysis of the energy budget for the flow to uncover the underlying physical mechanism. The yo-yoing of the mean-flow is shown to be driven by the elastic polymers injecting energy into the fluid and, in turn, being rotated by the large-scale mean shear. We then provide the mathematical model of the problem and solve it analytically, finding wave solutions with non-linear dispersion predicting the period of the yo-yoing and the parameter range where it occurs. As decaying mixing layers are one of the simplest and canonical examples of unsteady flows, the phenomenon identified here explains the anomalies recently observed in experiments of unsteady viscoelastic flows in complex geometries.