Kalogirou, A, Keaveny, EE and Papageorgiou, DT (2015) An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation. Proceeding of the Royal Society A, 471 (2179). ISSN 1364-5021
Abstract
The Kuramoto–Sivashinsky equation in one spatial dimension (1D KSE) is one of the most well-known and well-studied partial differential equations. It exhibits spatio-temporal chaos that emerges through various bifurcations as the domain length increases. There have been several notable analytical studies aimed at understanding how this property extends to the case of two spatial dimensions. In this study, we perform an extensive numerical study of the Kuramoto–Sivashinsky equation (2D KSE) to complement this analytical work. We explore in detail the statistics of chaotic solutions and classify the solutions that arise for domain sizes where the trivial solution is unstable and the long-time dynamics are completely two-dimensional. While we find that many of the features of the 1D KSE, including how the energy scales with system size, carry over to the 2D case, we also note several differences including the various paths to chaos that are not through period doubling.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, The Royal Society. This is an author produced version of a paper published in Proceeding of the Royal Society A. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | two-dimensional Kuramoto–Sivashinsky equation; spatio-temporal chaos; equipartition of energy |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Jul 2015 11:55 |
Last Modified: | 16 Nov 2016 09:46 |
Published Version: | http://dx.doi.org/10.1098/rspa.2014.0932 |
Status: | Published |
Publisher: | The Royal Society |
Identification Number: | 10.1098/rspa.2014.0932 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:88551 |