Numerical analysis of slender vortex motion

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Several numerical methods for slender vortex motion (the local induction equation, the Klein-Majda equation, and the Klein-Knio equation) are compared on the specific example of sideband instability of Kelvin waves on a vortex. Numerical experiments on this model problem indicate that all these methods yield qualitatively similar behavior, and this behavior is different from the behavior of a non-slender vortex with variable cross-section. It is found that the boundaries between stable, recurrent, and chaotic regimes in the parameter space of the model problem depend on the method used. The boundaries of these domains in the parameter space for the Klein-Majda ... continued below

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130 p.

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Zhou, H. February 1, 1996.

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Description

Several numerical methods for slender vortex motion (the local induction equation, the Klein-Majda equation, and the Klein-Knio equation) are compared on the specific example of sideband instability of Kelvin waves on a vortex. Numerical experiments on this model problem indicate that all these methods yield qualitatively similar behavior, and this behavior is different from the behavior of a non-slender vortex with variable cross-section. It is found that the boundaries between stable, recurrent, and chaotic regimes in the parameter space of the model problem depend on the method used. The boundaries of these domains in the parameter space for the Klein-Majda equation and for the Klein-Knio equation are closely related to the core size. When the core size is large enough, the Klein-Majda equation always exhibits stable solutions for our model problem. Various conclusions are drawn; in particular, the behavior of turbulent vortices cannot be captured by these local approximations, and probably cannot be captured by any slender vortex model with constant vortex cross-section. Speculations about the differences between classical and superfluid hydrodynamics are also offered.

Physical Description

130 p.

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OSTI as DE96011528

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  • Other Information: TH: Thesis (Ph.D.)

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  • Other: DE96011528
  • Report No.: LBL--38265
  • Grant Number: AC03-76SF00098
  • DOI: 10.2172/245550 | External Link
  • Office of Scientific & Technical Information Report Number: 245550
  • Archival Resource Key: ark:/67531/metadc667903

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  • February 1, 1996

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

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  • April 5, 2016, 12:34 p.m.

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Zhou, H. Numerical analysis of slender vortex motion, report, February 1, 1996; California. (digital.library.unt.edu/ark:/67531/metadc667903/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.