Jacquet, Q., Kim, E. and Hollerbach, R. (2018) Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows. Entropy, 20 (8). 613. ISSN 1099-4300
Abstract
We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing
non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, aswell as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent
PDFs, we calculate the information length (L), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length (L¥ = L(t ! ¥)) which maps out the underlying attractor structures, highlighting a unique property of L¥ which depends on the trajectory/history of a PDF’s evolution.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0). |
Keywords: | self-organisation; shear flows; coherent structures; turbulence; stochastic processes; Langevin equation; Fokker-Planck equation; information length |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Aug 2018 14:37 |
Last Modified: | 21 Aug 2018 14:44 |
Published Version: | https://doi.org/10.3390/e20080613 |
Status: | Published |
Publisher: | MDPI AG |
Refereed: | Yes |
Identification Number: | 10.3390/e20080613 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:134740 |