Linear instability in planar viscoelastic Taylor-Couette flow with and without explicit polymer diffusion

TL;DR

This paper shows that linear instability in planar viscoelastic Taylor-Couette flow only appears when polymer diffusion is artificially introduced, highlighting the role of numerical diffusion in generating chaotic flow behaviors.

Contribution

It demonstrates that the observed elastic turbulence is a numerical artifact caused by diffusive errors, not an inherent linear instability of the governing equations.

Findings

Linear instability requires added polymer diffusion.

Numerical discretization introduces diffusive errors near boundaries.

Chaotic flows can arise from diffusive errors in simulations.

Abstract

Elastic turbulence has been found in computations of planar viscoelastic Taylor-Couette flow using the Oldroyd-B model, apparently generated by a linear instability (van Buel et al. Europhys. Lett., 124, 14001, 2018). We demonstrate that no such linear instability exists in the governing equations used unless some diffusion is added to the polymer conformation tensor equation, as might occur through a diffusive numerical scheme. With this addition, the polymer diffusive instability (PDI) (Beneitez et al. (Phys. Rev. Fluids, 8, L101901, 2023)) exists and leads to chaotic flows resembling those found by van Buel et al. (2018). We show how finite volume or finite-difference discretisations of the governing equations can naturally introduce diffusive errors near boundaries which are sufficient to trigger PDI. This suggests that PDI could well be important in numerical solutions of wall-bounded viscoelastic flows modelled using Oldroyd-B and FENE-P even with no polymer stress diffusion explicitly included.