Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Nonlinear vortex trail dynamics. II. Analytic solutions


Authors: Chjan C. Lim and Lawrence Sirovich
Journal: Quart. Appl. Math. 51 (1993), 129-146
MSC: Primary 76C05
DOI: https://doi.org/10.1090/qam/1205942
MathSciNet review: MR1205942
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Abstract: Spatially periodic large amplitude solutions of the von Karman model are obtained in the neighborhood of singularities. These singularities correspond to vortex clusters in the physical plane. The quasi-periodic and unbounded solutions found analytically confirm earlier numerical work and show qualitative agreement with experimental observations of large-scale phenomena of vortex trails. Separatrices or heteroclinic orbits were explicitly found for an integrable approximate equation, which indicate that the von Karman model itself supports chaotic solutions.


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DOI: https://doi.org/10.1090/qam/1205942
Article copyright: © Copyright 1993 American Mathematical Society


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