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arXiv · 2509.26168

Localised Arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows

Theo A. Lewy·Rich R. Kerswell
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Abstract

Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et al. Phys. Rev. Lett. 125, 154501, 2020). As a step to confirming this theoretically, we identify spanwise-localised arrowhead travelling 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-localised travelling wave. Spanwise-symmetric and asymmetric localised 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 localised 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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Theo A. Lewy, Rich R. Kerswell. 2026-04-21. Localised Arrowheads: The building blocks of elastic turbulence in rectilinear, sheared polymer flows. https://doi.org/10.1103/vt5l-fpy6

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