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Stream Classification and Solubility of the Dispersion Equation for Piecewise Constant Vorticity
Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This thesis concerns the water wave problem corresponding to a piecewise constant vorticity function. There are several results connected to this field. In [1] the authors prove the existence of small-amplitude capillary-gravity water waves in the setting of unidirectional waves, and present an explicit form of the dispersion equation in the case when the vorticity function has two jumps. A two-layer model with constant but different vorticities is studied in [2], while in [3], an analysis of the dispersion equation for a three-layer model is given. In this thesis we first classify all stream solutions to the problem specified above, and then use our classification to prove and analyze solubility of the dispersion equation for a vorticity function with one jump. We do not require streams to be unidirectional (that is, we allow underlying counter-currents and internal stagnation).

Place, publisher, year, edition, pages
2018. , p. 27
Keywords [en]
Water waves, stream solutions, dispersion equation.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-146205ISRN: LiTH-MAT-EX--2018/04--SEOAI: oai:DiVA.org:liu-146205DiVA, id: diva2:1194226
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2018-04-10 Created: 2018-03-29 Last updated: 2018-05-08Bibliographically approved

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Stream Classification and Solubility of the Dispersion Equation for Piecewise Constant Vorticity(3662 kB)42 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf