Catastrophe models for the flow around immersed bodies.
DOI:
https://doi.org/10.24850/j-tyca-2010-01-01Keywords:
catastrophe theory applications, catastrophe theory, flow around immersed bodies, hysteresis in fluid mechanics, fluid mechanics, cusp catastropheAbstract
In fluid mechanics there are several phenomena that exhibit a hysteretic behavior and sudden changes not only of a quantitative, but also a qualitative nature. Such phenomena can be represented and explained by the catastrophe theory, which explains this kind of behavior observed in some physical systems. This article offers an analytical demonstration that the flow around immersed cylinders is a fold catastrophe. Extending this result, now with a semi-empirical approach, it can be shown that flow around cylinders and spheres with roughness can be represented using a cusp catastrophe geometry. Both results support the hypothesis that the flow around objects immersed in liquids can be modeled through catastrophe geometries and hence explain the occurrence of bifurcation, bimodality, sudden jumps and hysteresis.
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