Please use this identifier to cite or link to this item:
Full metadata record
DC FieldValueLanguage
dc.contributor.authorCotter, CJ-
dc.contributor.authorEldering, J-
dc.contributor.authorHolm, DD-
dc.contributor.authorJacobs, HO-
dc.contributor.authorMeier, DM-
dc.identifier.citationJournal of Nonlinear Science, (2016)en_US
dc.description.abstractWe review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles (essentially by moving the points). We then augment our dual pair by considering the action of diffeomorphisms on Taylor series, also known as jets. The augmented weak dual pairs induce a hierarchy of particle-like solutions and conservation laws with particles carrying a copy of a jet group. We call these augmented particles jetlets. The jet groups serve as finite-dimensional models of the diffeomorphism group itself, and so the jetlet particles serve as a finite-dimensional model of the self-similarity exhibited by ideal incompressible fluids. The conservation law associated to jetlet solutions is shown to be a shadow of Kelvin’s circulation theorem. Finally, we study the dynamics of infinite time particle mergers. We prove that two merging particles at the zeroth level in the hierarchy yield dynamics which asymptotically approach that of a single particle in the first level in the hierarchy. This merging behavior is then verified numerically as well as the exchange of angular momentum which must occur during a near collision of two particles. The resulting particle-like solutions suggest a new class of meshless methods which work in dimensions [Math Processing Error] n≥2 and which exhibit a shadow of Kelvin’s circulation theorem. More broadly, this provides one of the first finite-dimensional models of self-similarity in ideal fluids.en_US
dc.subjectRegularized fluidsen_US
dc.subjectHamiltonian mechanicsen_US
dc.subjectGeometric mechanicsen_US
dc.subjectDual pairsen_US
dc.titleWeak dual pairs and Jetlet methods for ideal incompressible fluid models in n≥2 dimensionsen_US
dc.relation.isPartOfJournal of Nonlinear Science-
Appears in Collections:Dept of Mathematics Research Papers

Files in This Item:
File Description SizeFormat 
Fulltext.pdf1.58 MBAdobe PDFView/Open

Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.