Unstable fixed points, heteroclinic cycles and exponential tails in turbulence production

Emily Stone; Philip Holmes

doi:10.1016/0375-9601(91)90503-Z

Unstable fixed points, heteroclinic cycles and exponential tails in turbulence production

Emily Stone, Philip Holmes

Mathematics

Cornell University

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

We show that solutions of ordinary differential equations possessing attracting heteroclinic cycles and subject to small random or periodic perturbations typically exhibit sharp events whose separations are well characterized by a probability distribution with an exponential tail. We review experimental evidence for such distributions in turbulent flows and indicate how our simple theory might be used to identify instability mechanisms.

Original language	English
Pages (from-to)	29-42
Number of pages	14
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	155
Issue number	1
DOIs	https://doi.org/10.1016/0375-9601(91)90503-Z
State	Published - Apr 29 1991

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title = "Unstable fixed points, heteroclinic cycles and exponential tails in turbulence production",

abstract = "We show that solutions of ordinary differential equations possessing attracting heteroclinic cycles and subject to small random or periodic perturbations typically exhibit sharp events whose separations are well characterized by a probability distribution with an exponential tail. We review experimental evidence for such distributions in turbulent flows and indicate how our simple theory might be used to identify instability mechanisms.",

author = "Emily Stone and Philip Holmes",

note = "Funding Information: * Research partially supported by AFOSR 0226A (Wall i.ay-ers) and the UK Science and Engineering Research Council.",

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AU - Holmes, Philip

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PY - 1991/4/29

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N2 - We show that solutions of ordinary differential equations possessing attracting heteroclinic cycles and subject to small random or periodic perturbations typically exhibit sharp events whose separations are well characterized by a probability distribution with an exponential tail. We review experimental evidence for such distributions in turbulent flows and indicate how our simple theory might be used to identify instability mechanisms.

AB - We show that solutions of ordinary differential equations possessing attracting heteroclinic cycles and subject to small random or periodic perturbations typically exhibit sharp events whose separations are well characterized by a probability distribution with an exponential tail. We review experimental evidence for such distributions in turbulent flows and indicate how our simple theory might be used to identify instability mechanisms.

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Unstable fixed points, heteroclinic cycles and exponential tails in turbulence production

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