Viscoelasticity-induced pulsatile motion of 2D roll cell in laminar wall-bounded shear flow

TL;DR

This study investigates how viscoelasticity causes pulsatile, unsteady motion in 2D roll cells within laminar shear flow, revealing a new dynamic behavior linked to polymer effects and flow stability.

Contribution

It demonstrates that viscoelasticity induces periodic pulsations in 2D roll cells, driven by a time lag in viscoelastic force response, distinct from relaxation time scaling.

Findings

Viscoelasticity causes periodic pulsations in 2D roll cells.

Pulsation period scales with cell turnover time, not relaxation time.

Flow stability and energy balance are affected by viscoelastic effects.

Abstract

For the clarification of the routes to elasto-inertial turbulence (EIT), it is essential to understand how viscoelasticity modulates coherent flow structures including the longitudinal vortices. We focused on a rotating plane Couette flow that provides two-dimensional (2D) roll cells for the steady laminar Newtonian-fluid case, and we investigated how the steady longitudinal vortices are modulated by viscoelasticity at different Weissenberg numbers. The viscoelasticity was found to induce an unsteady flow state where the 2D roll-cell structure was periodically enhanced and damped with a constant period, keeping the homogeneity in the streamwise direction. This pulsatile motion of the roll cell was caused by a time lag in the response of the viscoelastic force to the vortex development. Both the pulsation period and time lag were found to be scaled by the turnover time of cell rotation rather than by the relaxation time, despite the viscoelasticity-induced instability. We also discuss the counter torque on the roll cell and the net energy balance, considering their relevance to polymer drag reduction and EIT.