Imperial College London
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ProfessorColinCotter

Faculty of Natural Sciences, Department of Mathematics

Professor of Computational Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3468colin.cotter

 
 
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Location

 

755Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Cotter:2016:10.1007/s00332-016-9317-6,
author = {Cotter, CJ and Eldering, J and Holm, DD and Jacobs, HO and Meier, DM},
doi = {10.1007/s00332-016-9317-6},
journal = {Journal of Nonlinear Science},
pages = {1723--1765},
title = {Weak dual pairs and jetlet methods for ideal incompressible fluid models in n >= 2 dimensions},
url = {http://dx.doi.org/10.1007/s00332-016-9317-6},
volume = {26},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We 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 n≥2n≥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.
AU  - Cotter,CJ
AU  - Eldering,J
AU  - Holm,DD
AU  - Jacobs,HO
AU  - Meier,DM
DO  - 10.1007/s00332-016-9317-6
EP  - 1765
PY  - 2016///
SN  - 1432-1467
SP  - 1723
TI  - Weak dual pairs and jetlet methods for ideal incompressible fluid models in n >= 2 dimensions
T2  - Journal of Nonlinear Science
UR  - http://dx.doi.org/10.1007/s00332-016-9317-6
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000386609600005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/43430
VL  - 26
ER  -
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