Competing instabilities in wide-gap viscoelastic Taylor-Couette flow: Taylor vs. helical vortices
Abstract
This paper presents a numerical study of the stability of a polymer solution flow between concentric cylinders with a rotating inner cylinder. The case of a small-radius inner cylinder is considered. The fluid motion is described using a specific case of the Kelvin-Voigt model, often referred to as the Oskolkov model. This model is applicable to very dilute polymer solutions, where the retardation time is much smaller than the characteristic time of the problem and elastic forces are much smaller than viscous forces. The stability of the steady-state motion is investigated using a fully nonlinear approach by means of direct numerical simulation of a perturbation introduced as finite-duration white noise. Depending on the Reynolds number, the perturbation either decays or grows. The critical Reynolds numbers obtained for both Newtonian and non-Newtonian fluids are found to be in agreement with the predictions of the linear theory. It is also shown that an increase in the elastic forces makes helical perturbations more dangerous than their axisymmetric counterparts.
Related
- Comment on "Note on the start-up of Couette flow for viscoelastic fluids" [Phys. Fluids 35, 113108 (2023)]
- Nonlinear dynamics of short-wave instabilities in a helical vortex within and beyond the weakly nonlinear regime
- Thermosolutal Marangoni instabilities in a weakly viscoelastic falling film with soluble surfactant
- Interaction-driven competing instabilities in two-dimensional checkerboard quadratic band crossing semimetals
- Competing charge and spin instabilities and giant magnetoelastic coupling in CrSb
BibTeX
@misc{proskurin2026competing,
title = {{Competing instabilities in wide-gap viscoelastic Taylor-Couette flow: Taylor vs. helical vortices}},
author = {Alexander Proskurin},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29552},
eprint = {2608.29552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29552},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Competing instabilities in wide-gap viscoelastic Taylor-Couette flow: Taylor vs. helical vortices
AU - Alexander Proskurin
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29552
UR - https://arxiv.org/abs/2608.29552
AB - This paper presents a numerical study of the stability of a polymer solution flow between concentric cylinders with a rotating inner cylinder. The case of a small-radius inner cylinder is considered. The fluid motion is described using a specific case of the Kelvin-Voigt model, often referred to as the Oskolkov model. This model is applicable to very dilute polymer solutions, where the retardation time is much smaller than the characteristic time of the problem and elastic forces are much smaller than viscous forces. The stability of the steady-state motion is investigated using a fully nonlinear approach by means of direct numerical simulation of a perturbation introduced as finite-duration white noise. Depending on the Reynolds number, the perturbation either decays or grows. The critical Reynolds numbers obtained for both Newtonian and non-Newtonian fluids are found to be in agreement with the predictions of the linear theory. It is also shown that an increase in the elastic forces makes helical perturbations more dangerous than their axisymmetric counterparts.
ER -