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Download Bifurcations in Flow Patterns: Some Applications of the by P.G. Bakker PDF

By P.G. Bakker

The major inspiration of the current research is to illustrate that the qualitative thought of diffe­ rential equations, whilst utilized to difficulties in fluid-and gasdynamics, will give a contribution to the knowledge of qualitative elements of fluid flows, particularly these involved in geometrical homes of movement fields reminiscent of form and balance of its streamline styles. it truly is noticeable that perception into the qualitative constitution of circulation fields is of significant value and looks as an final goal of circulate study. Qualitative perception models our understand­ ledge and serves as an outstanding advisor for extra quantitative investigations. in addition, quali­ tative details can turn into very worthy, specially while it really is utilized in shut corres­ pondence with numerical equipment, for you to interpret and cost numerical effects. A qualitative research should be an important for the research of the move within the neighbourhood of singularities the place a numerical process isn't trustworthy anymore as a result of discretisation er­ rors being unacceptable. Up until now, common examine tools -frequently in response to rigorous analyses, cautious nu­ merical techniques and complicated experimental options -have elevated considera­ bly our qualitative wisdom of flows, albeit that the data is frequently got ultimately by means of a means of a cautious yet bulky exam of quantitative info. some time past decade, new equipment are less than improvement that yield the qualitative infor­ mation extra at once. those tools, utilize the data on hand within the qualitative concept of differen­ tial equations and within the idea of bifurcations.

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Extra resources for Bifurcations in Flow Patterns: Some Applications of the Qualitative Theory of Differential Equations in Fluid Dynamics

Sample text

In that way the knowledge about different types of conical stagnation points contribute to the understanding of the topology of conical flow patterns of increasing complexity. To obtain a certain familiarity with the characteristic features of conical flow topology we proceed by discussing first the most simple example of a conical flow: the uniform parallel flow. Consider a uniform parallel flow with a constant velocity lloo in the positive x-direction. This flow will be considered in the cross flow plane l:.

The coordinate system is chosen with its origin in a conical stagnation point. The following series expansion of the conical potential is used 1

Various types of flow patterns may be observed in the vicinity of conical stagnation points. ). Furthermore, a conical stagnation line or a starlike node can be encountered in special cases. CHAPTER II 52 - Finally, there is a strong evidence that conical flow patterns may be structurally unstable leading to local bifurcation involving the generation or disappearance of conical stagnation points. Due to their sensitivity to perturbations the corresponding structural unstable flow patterns are hardly to realize in experiments or by numerical computations.

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