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Two cylindrical vortex sheets : evolution and singularity formation


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/17434

Two cylindrical vortex sheets : evolution and singularity formation

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dc.contributor.author Jeremy, Johnson
dc.date.accessioned 2012-02-01T17:19:14Z
dc.date.available 2012-02-01T17:19:14Z
dc.date.issued 2012-02-01
dc.date.submitted May 2011
dc.identifier.uri http://hdl.handle.net/1928/17434
dc.description.abstract Using 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.iso en_US en_US
dc.subject singularity formation en_US
dc.subject vortex sheets en_US
dc.subject roll-up en_US
dc.subject.lcsh Vortex-motion--Mathematical models.
dc.subject.lcsh Turbulence--Mathematical models.
dc.subject.lcsh Fluid flow--Mathematical models.
dc.title Two cylindrical vortex sheets : evolution and singularity formation en_US
dc.type Thesis en_US
dc.description.degree Mathematics en_US
dc.description.level Masters en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor Nitsche, Monika
dc.description.committee-member Nitsche, Monika
dc.description.committee-member Embid, Pedro
dc.description.committee-member Lorenz, Jens

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