Lyapunov dimension of elastic turbulence
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...
| Main Authors: | , , , |
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| Format: | Journal article |
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Cambridge University Press
2017
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| _version_ | 1797095727389736960 |
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| author | Plan, E Gupta, A Vincenzi, D Gibbon, J |
| author_facet | Plan, E Gupta, A Vincenzi, D Gibbon, J |
| author_sort | Plan, E |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:32:01Z |
| format | Journal article |
| id | oxford-uuid:cea688d6-655c-4dfc-9f87-931a1094c28a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:32:01Z |
| publishDate | 2017 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:cea688d6-655c-4dfc-9f87-931a1094c28a2022-03-27T07:37:05ZLyapunov dimension of elastic turbulenceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cea688d6-655c-4dfc-9f87-931a1094c28aSymplectic Elements at OxfordCambridge University Press2017Plan, EGupta, AVincenzi, DGibbon, JLow-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. |
| spellingShingle | Plan, E Gupta, A Vincenzi, D Gibbon, J Lyapunov dimension of elastic turbulence |
| title | Lyapunov dimension of elastic turbulence |
| title_full | Lyapunov dimension of elastic turbulence |
| title_fullStr | Lyapunov dimension of elastic turbulence |
| title_full_unstemmed | Lyapunov dimension of elastic turbulence |
| title_short | Lyapunov dimension of elastic turbulence |
| title_sort | lyapunov dimension of elastic turbulence |
| work_keys_str_mv | AT plane lyapunovdimensionofelasticturbulence AT guptaa lyapunovdimensionofelasticturbulence AT vincenzid lyapunovdimensionofelasticturbulence AT gibbonj lyapunovdimensionofelasticturbulence |