Uncertainty in elastic turbulence

King, Jack R.C., Poole, Robert J., Fonte, Cláudio P. and Lind, Steven J. 2025. Uncertainty in elastic turbulence. Journal of Fluid Mechanics 1020 , A2. 10.1017/jfm.2025.10546

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Abstract

Elastic turbulence can lead to increased flow resistance, mixing and heat transfer. Its control – either suppression or promotion – has significant potential, and there is a concerted ongoing effort by the community to improve our understanding. Here we explore the dynamics of uncertainty in elastic turbulence, inspired by an approach recently applied to inertial turbulence in Ge et al. (J. Fluid Mech., vol. 977, 2023, A17). We derive equations for the evolution of uncertainty measures, yielding insight on uncertainty growth mechanisms. Through numerical experiments, we identify four regimes of uncertainty evolution, characterised by (i) rapid transfer to large scales, with large-scale growth rates of τ6 (where τ represents time), (ii) a dissipative reduction of uncertainty, (iii) exponential growth at all scales and (iv) saturation. These regimes are governed by the interplay between advective and polymeric contributions (which tend to increase uncertainty), viscous, relaxation and dissipation effects (which reduce uncertainty) and inertial contributions. In elastic turbulence, reducing Reynolds number increases uncertainty at short times, but does not significantly influence the growth of uncertainty at later times. At late times, the growth of uncertainty increases with Weissenberg number, with decreasing polymeric diffusivity and with the logarithm of the maximum length scale, as large flow features adjust the balance of advective and relaxation effects. These findings provide insight into the dynamics of elastic turbulence, offering a new approach for the analysis of viscoelastic flow instabilities.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Engineering
Additional Information:	License information from Publisher: LICENSE 1: URL: https://creativecommons.org/licenses/by/4.0/, Type: open-access
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date of First Compliant Deposit:	1 October 2025
Date of Acceptance:	3 August 2025
Last Modified:	01 Oct 2025 10:15
URI:	https://orca.cardiff.ac.uk/id/eprint/181431

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