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Lyapunov dimension of elastic turbulence

Published online by Cambridge University Press:  06 June 2017

Emmanuel Lance Christopher VI M. Plan Open the ORCID record for Emmanuel Lance Christopher VI M. Plan [Opens in a new window] ,
Anupam Gupta ,
Dario Vincenzi  and
John D. Gibbon
Emmanuel Lance Christopher VI M. Plan*
Affiliation:
Université Côte d’Azur, CNRS, LJAD, 06108 Nice, France
Anupam Gupta
Affiliation:
FERMaT, Université de Toulouse, CNRS, INPT, INSA, UPS, 31062 Toulouse, France
Dario Vincenzi
Affiliation:
Université Côte d’Azur, CNRS, LJAD, 06108 Nice, France
John D. Gibbon
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: elcplan@unice.fr
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Abstract

Low-Reynolds-number polymer solutions exhibit a chaotic behaviour known as ‘elastic turbulence’ when the Weissenberg number exceeds a critical value. The two-dimensional Oldroyd-B model is the simplest constitutive model that reproduces this phenomenon. To make a practical estimate of the resolution scale of the dynamics, one requires the assumption that an attractor of the Oldroyd-B model exists; numerical simulations show that the quantities on which this assumption is based are bounded. We estimate the Lyapunov dimension of this assumed attractor as a function of the Weissenberg number by combining a mathematical analysis of the model with direct numerical simulations.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Non-Newtonian Flows: Viscoelasticity

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Rapids
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Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , R4
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© 2017 Cambridge University Press 

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