Lyapunov dimension of elastic turbulence
File(s)
Accepted version
Author(s)
Plan, ELCM
Gupta, A
Vincenzil, D
Gibbons, JD
Type
Journal Article
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.
Date Issued
2017-06-06
Date Acceptance
2017-04-20
Citation
Journal of Fluid Mechanics, 2017, 822
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Journal / Book Title
Journal of Fluid Mechanics
Volume
822
Copyright Statement
© 2017 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
nonlinear dynamical systems
viscoelasticity
NAVIER-STOKES EQUATIONS
VISCOELASTIC FLOWS
ATTRACTOR DIMENSION
POLYMER-SOLUTION
DIFFUSION
INSTABILITIES
STABILITY
EXISTENCE
DYNAMICS
NUMBERS
Publication Status
Published
Article Number
R4