Covariant Lyapunov vectors of chaotic Rayleigh-Benard convection

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dc.contributor.authorXu, M.en
dc.contributor.authorPaul, Mark R.en
dc.date.accessioned2024-10-10T14:35:58Zen
dc.date.available2024-10-10T14:35:58Zen
dc.date.issued2016-06-10en
dc.description.abstractWe explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time-dependent Boussinesq equations for a convection layer in a shallow square box geometry with an aspect ratio of 16 for very long times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. The dynamics explored has fractal dimensions of 20?Dλ?50, and we compute on the order of 150 covariant Lyapunov vectors. We use the covariant Lyapunov vectors to quantify the degree of hyperbolicity of the dynamics and the degree of Oseledets splitting and to explore the temporal and spatial dynamics of the Lyapunov vectors. Our results indicate that the chaotic dynamics of Rayleigh-Bénard convection is nonhyperbolic for all of the Rayleigh numbers we have explored. Our results yield that the entire spectrum of covariant Lyapunov vectors that we have computed are tangled as indicated by near tangencies with neighboring vectors. A closer look at the spatiotemporal features of the Lyapunov vectors suggests contributions from structures at two different length scales with differing amounts of localization.en
dc.description.versionPublished versionen
dc.format.extent12 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 062208 (Article number)en
dc.identifier.doihttps://doi.org/10.1103/PhysRevE.93.062208en
dc.identifier.eissn2470-0053en
dc.identifier.issn2470-0045en
dc.identifier.issue6en
dc.identifier.orcidPaul, Mark [0000-0002-0701-1955]en
dc.identifier.pmid27415256en
dc.identifier.urihttps://hdl.handle.net/10919/121323en
dc.identifier.volume93en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000377508500002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleCovariant Lyapunov vectors of chaotic Rayleigh-Benard convectionen
dc.title.serialPhysical Review Een
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Mechanical Engineeringen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Engineering/COE T&R Facultyen

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