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Modeling ripple formation

dc.contributor.advisorNeugebauer, Horst J.
dc.contributor.authorKüpper, Michael
dc.description.abstractThe aim of this thesis was to approach the problem of ripple formation by a model which describes the phenomenon on a macroscopic scale and does not incorporate the detailed dynamics of the fluid flow field. We developed a parameterization called shadow, which depends only on the negative curvature of the current bed surface. Since the shadow-function is part of a coupled differential equation this approach is non--local. We assert that this non--locality is inevitable to model the characteristic fluid field. Although we avoid back coupling of bedforms to the dynamics of the fluid flow, which seems to be a great simplification of these kinds of models, the resulting shape and their evolution is surprisingly realistic. Furthermore, this approach enables us to simulate the long time and large spatial scale evolution of ripples, which we are hardly able to achieve in natural experiments. Our model supports the idea that the mechanism of ripple formation is not strongly affected by the details of the complex flow structures (Nishimori et al. 1998).
Defina (2003) states that the numerical simulation of ripple generation and development in a direct way and on a macroscopic scale could provide the missing link between experimental investigations and simplified theories, offering a valuable tool for bottom morphology investigations. The results discussed in the thesis support this assumption and reveal the ability of numerical modeling. Since the main mechanisms of ripple formation are well reproduced by the model, among the complex converging and diverging, our minimal model may be considered as a significant step toward the comprehensive understanding of large scale evolution processes of ripples. The main disagreement concerns the apparent lack of stable equilibrium conditions for the wavelength, due to the sensitivity to perturbations. The whole model approach is based on the assumption that it is possible to simulate the pattern formation only depending on surface attributes. This implies that any change of the flow conditions first rearranges the bed relief before new regular bedforms could develop. Hence our model underlines that ripple formation is not only the result of flow structures, which are simply imprinted on the river bed, but also an effect of ripple interaction.
dc.rightsIn Copyright
dc.subjectPattern formation
dc.subject.ddc500 Naturwissenschaften
dc.subject.ddc530 Physik
dc.subject.ddc550 Geowissenschaften
dc.titleModeling ripple formation
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeHördt, Andreas

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