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  • Letter
  • Open Access

Localized arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows

Theo A. Lewy* and Rich R. Kerswell

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

  • *Contact author: tal43@cam.ac.uk
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Phys. Rev. Fluids 11, L051301 – Published 15 May, 2026

DOI: https://doi.org/10.1103/vt5l-fpy6

Abstract

Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organized around the interactions of localized versions of two-dimensional (2D) “arrowhead” traveling waves [J. Page et al. Phys. Rev. Lett. 125, 154501 (2020)]. As a step to confirming this theoretically, we identify spanwise-localized arrowhead traveling waves by tracking a symmetry-breaking bifurcation of the known spanwise-invariant (2D) arrowhead to a spanwise-periodic state and then discovering a secondary modulational instability to a spanwise-localized traveling wave. Spanwise-symmetric and -asymmetric localized arrowheads exist with the latter having a phase speed slightly inclined to the streamwise direction. Computations capture the flow randomly switching between spanwise local and global arrowhead states in a streamwise-restricted domain, suggesting they form the building blocks of the chaos. Splitting events are also seen, in which a single localized state spawns multiple arrowheads. However, both cross-shear and spanwise velocities are small, suggesting that this elastic turbulence will not be a good mixer.

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Phys. Rev. Fluids 11, L051301– Published 15 May, 2026
  • Received 1 October 2025
  • Accepted 20 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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