# The coherent structures of EVP fluid flow past a circular cylinder

## TL;DR

This study explores how elasticity and plasticity affect fluid flow around a cylinder, revealing how these properties influence flow patterns and complexity.

## Contribution

The paper introduces a detailed analysis of viscoelastic and elastoviscoplastic fluid behavior using advanced decomposition techniques.

## Key findings

- Increasing the Weissenberg number elongates the recirculation bubble in viscoelastic fluids.
- Stronger plastic effects, especially with n ≥ 1, increase flow complexity in EVP fluids.
- Three dynamic regimes are identified: periodic, transitional, and fully complex.

## Abstract

This study investigates the impact of elasticity and plasticity on two-dimensional flow past a circular cylinder at Reynolds number \documentclass[12pt]{minimal}
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\begin{document}$$Re = 100$$\end{document}Re=100. Ten direct numerical simulations were performed using the Saramito-Herschel–Bulkley model to represent viscoelastic and elastoviscoplastic (EVP) fluids. The flow evolves from a periodic von Kármán vortex street to chaotic-like regimes. Proper Orthogonal Decomposition (POD) and Higher Order Dynamic Mode Decomposition (HODMD) are applied to extract dominant flow structures and their temporal dynamics. For viscoelastic fluids, increasing the Weissenberg number Wi elongates the recirculation bubble and shifts it downstream, resulting in more intricate but still periodic behavior. In EVP fluids, seven cases explore variations in Bingham number Bn, solvent viscosity ratio \documentclass[12pt]{minimal}
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\begin{document}$$\beta _s$$\end{document}βs, and power law index n, aiming to qualitatively assess their influence rather than determine critical thresholds. Results indicate that stronger plastic effects, especially with \documentclass[12pt]{minimal}
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\begin{document}$$n \ge 1$$\end{document}n≥1, lead to increased flow complexity. Three dynamic regimes are identified: (i) periodic; (ii) transitional, with elongated recirculation and disrupted periodicity; and (iii) fully complex, with breakdown of recirculation. Overall, the study highlights the interplay between inertia, elasticity, and yield stress in non-Newtonian flows past obstacles and identifies key parameters driving the transition from periodic to complex regimes.