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dc.contributor.authorJeremy, Johnson
dc.date.accessioned2012-02-01T17:19:14Z
dc.date.available2012-02-01T17:19:14Z
dc.date.issued2012-02-01
dc.date.submittedMay 2011
dc.identifier.urihttp://hdl.handle.net/1928/17434
dc.description.abstractUsing Rosenhead's point-vortex approximation with correction terms, the evolution of two symmetrical, counter-rotating, initially cylindrical vortex sheets in an incompressible, potential fluid flow is studied. Simulations are performed in time up to the occurrence of branch-point curvature singularities in the vortex sheets' geometries. The numerical methods employed are discussed. Parameters pertaining to the asymptotics of the Fourier coefficients of the vortex sheets' positions are numerically fitted to gain insight into aspects of the singularity formation; these include the order of the branch-point singularities, and the times and locations of singularity formation. A smoothing over initial singularity formations is implemented by either the heat equation or through a local application of the vortex blob method in an attempt to gain details into further singularity formations. Lastly, the effects of the initially prescribed total circulation around the vortex sheets on their evolutions are studied, both up to the time of singularity formation, and with the implementation of the vortex blob method, past the times of singularity formation.en_US
dc.language.isoen_USen_US
dc.subjectsingularity formationen_US
dc.subjectvortex sheetsen_US
dc.subjectroll-upen_US
dc.subject.lcshVortex-motion--Mathematical models.
dc.subject.lcshTurbulence--Mathematical models.
dc.subject.lcshFluid flow--Mathematical models.
dc.titleTwo cylindrical vortex sheets : evolution and singularity formationen_US
dc.typeThesisen_US
dc.description.degreeMathematicsen_US
dc.description.levelMastersen_US
dc.description.departmentUniversity of New Mexico. Dept. of Mathematics and Statisticsen_US
dc.description.advisorNitsche, Monika
dc.description.committee-memberNitsche, Monika
dc.description.committee-memberEmbid, Pedro
dc.description.committee-memberLorenz, Jens


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