Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Bounded and unbounded solutions of the von Kármán vortex trail


Authors: Chjan Lim and Lawrence Sirovich
Journal: Quart. Appl. Math. 47 (1989), 447-458
MSC: Primary 76C05
DOI: https://doi.org/10.1090/qam/1012269
MathSciNet review: MR1012269
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Abstract | References | Similar Articles | Additional Information

Abstract: The general initial value problem for the linearized von Karman vortex trail is solved. In particular, the fundamental differences between von Karman's normal mode solutions and aperiodic solutions with compact support are discussed. Within the natural space $ {\ell _2}$, it is shown that the von Karman trail at its special aspect ratio (neutrally stable case) supports unbounded solutions. Two invariants of the equations determine whether a solution is bounded or unbounded. The asymptotic behaviour of aperiodic solutions is discussed. It is found that unbounded solutions grow at the rate $ O\left( {ln \tau } \right)$ in $ {\ell _\infty }$ while bounded solutions decay as $ O\left( {1/\sqrt \tau } \right)$. In addition, a Loschmidt's demon is constructed for the reversible dispersive equations which demonstrates the focussing effect in the von Karman trail.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1012269
Article copyright: © Copyright 1989 American Mathematical Society


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