The subject of motions in two-dimensional ideal fluids is treated by numerical methods and the results given an interpretation based on theories as well as numerical experiments. Phenomena in ideal fluids have relevance to flows in realistic fluids when the flow speeds encountered are much smaller than the speed of sound and when dissipative mechanisms play a negligible role. The restriction to consider only motions of two dimensions is established and the resulting mathematical description yields a classical formalism. In terms of the scalar vorticity the motion of a two-dimensional ideal fluid can be interpreted by the flow in phase space of a classical phase fluid. The scalar stream function acts as a Hamiltonian for a system whose phase space corresponds to real space. Two models with respectively an infinite and a finite number of degrees of freedom are used to picture the evolution with time of the vorticity distribution. The former model, the field model, is used in analytic studies, and the latter model, the particle model, is employed in the numerical approach. The field model is reviewed as an introduction to the subject. The particle model is fitted into a numerical scheme that forms the basis of a computer simulation code VORTEX. This numerical scheme is presented in detail and made the subject of a numerical analysis. Controlled numerical experiments are carried out to establish possible inaccuracies of the scheme and the sources of these inaccuracies are revealed by means of the results from the numerical analysis. The general work of preparing controlled numerical experiments is briefly mentioned and by recording the experience from several numerical experiments the quality of these can be assessed. Results of several numerical experiments are then presented. The problem of two-dimensional turbulence is tackled by a precursory study of the interaction between finite area vorticity regions. An analytic calculation is made to support the numerical simulations which demonstrate the non-linear aspects of vortex interactions: fusion of strongly interacting vortices of the same sign and large amplitude oscillations in the flow from two vortices of opposite sign. The numerical experiments that follow, treat the stability and long-time evolution of laminar wakes, and heuristic comparisons are made with wind tunnel experiments that minimise three-dimensional effects. A model of four finite-sized vortices is used to study the stability of von Kármán vortex streets. Comparisons with theory are made and the results show fusion of like-signed vortex regions as well as fission of a vortex in the presence of other vortices. The final study comprises numerical experiments with a model approximating vortex flows in jets. It is concluded that much insight can be gained by using relatively simple flow models combined with suitable numerical scheme in order to understand the non-linear dynamics of vortex flows.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:451452 |
| Date | January 1973 |
| Creators | Christiansen, Jes Peter |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/74486/ |
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