Extensive Chaos in The Lorenz-96 Model

dc.contributorVirginia Techen
dc.contributor.authorKarimi, A.en
dc.contributor.authorPaul, Mark R.en
dc.contributor.departmentMechanical Engineeringen
dc.contributor.departmentBiomedical Engineering and Mechanicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:19Zen
dc.date.available2014-04-09T18:12:19Zen
dc.date.issued2010-12-01en
dc.description.abstractWe explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and the deviation from extensivity decreases nonmonotonically with increasing system size. The length scale describing the deviations from extensivity is consistent with the natural chaotic length scale in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. We find that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom. As the forcing is increased, at constant system size, the dimension density grows monotonically and saturates at a value less than unity. We use this to quantify the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns. (C) 2010 American Institute of Physics. [doi:10.1063/1.3496397]en
dc.description.sponsorshipNSF CBET-0747727en
dc.identifier.citationKarimi, A.; Paul, M. R., "extensive chaos in the lorenz-96 model," Chaos 20, 043105 (2010); http://dx.doi.org/10.1063/1.3496397en
dc.identifier.doihttps://doi.org/10.1063/1.3496397en
dc.identifier.issn1054-1500en
dc.identifier.urihttp://hdl.handle.net/10919/47045en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/chaos/20/4/10.1063/1.3496397en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectRayleigh-bénard convectionen
dc.subjectTurbulenceen
dc.subjectDimensionen
dc.subjectExponentsen
dc.subjectPredictabilityen
dc.subjectAttractorsen
dc.subjectTransitionsen
dc.subjectFlowen
dc.titleExtensive Chaos in The Lorenz-96 Modelen
dc.title.serialChaosen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
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