A study of short wave instability on vortex filaments

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The numerical stability and accuracy of the vortex method are studied. The effect of the ordinary differential equations (ODE) solver and of the time step on the numerical stability is analyzed. Various ODE solvers are compared and a best performer is chosen. A new constraint on the time step based on numerical stability is proposed and verified in numerical simulations. It is shown through numerical examples that empirical rules for selecting the spatial discretization obtained in simple test problems may not be extended to more general problems. The thin tube vortex filament method is applied to the problem of Widnall`s ... continued below

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161 p.

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Wang, Hong Yun December 1, 1996.

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The numerical stability and accuracy of the vortex method are studied. The effect of the ordinary differential equations (ODE) solver and of the time step on the numerical stability is analyzed. Various ODE solvers are compared and a best performer is chosen. A new constraint on the time step based on numerical stability is proposed and verified in numerical simulations. It is shown through numerical examples that empirical rules for selecting the spatial discretization obtained in simple test problems may not be extended to more general problems. The thin tube vortex filament method is applied to the problem of Widnall`s instability on vortex rings. Numerical results different from previous calculations are presented and the source of the discrepancies is explained. The long time behavior of the unstable mode on thin vortex rings is simulated and analyzed. The short wave instability on vortex filaments is investigated both theoretically and numerically. It is shown that the short wave instability always occurs on co-rotating vortex filaments of fixed core structure. Furthermore when they are close to each other, vortex filaments produce short wave unstable modes which lead to wild stretching and folding. However, when the inter-filament distance is large in comparison with the core size of the filaments, unstable modes are bounded by a small fraction of the core size and the vortex filaments do not create hairpins nor wild stretching. These findings may explain the smooth behavior of the superfluid vortices. The formation of hairpin structures on numerical vortex filaments is investigated. It is shown that the formation of hairpin structures is independent of the ODE solver, of the time step and of other numerical parameters. The hairpin structures are primarily caused by short wave instability on co-rotating vortex filaments.

Physical Description

161 p.

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OSTI as DE97004235

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

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  • Other: DE97004235
  • Report No.: LBNL--39721
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 451206
  • Archival Resource Key: ark:/67531/metadc679999

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • December 1, 1996

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  • July 25, 2015, 2:21 a.m.

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  • April 5, 2016, 12:31 p.m.

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Wang, Hong Yun. A study of short wave instability on vortex filaments, thesis or dissertation, December 1, 1996; California. (digital.library.unt.edu/ark:/67531/metadc679999/: accessed October 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.