Passive scalars and three-dimensional Liouvillian maps

Julyan H.E. Cartwright; Mario Feingold; Oreste Piro

doi:10.1016/0167-2789(94)90247-X

Passive scalars and three-dimensional Liouvillian maps

Julyan H.E. Cartwright, Mario Feingold, Oreste Piro

Department of Physics

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23 Scopus citations

Abstract

Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrible cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.

Original language	English
Pages (from-to)	22-33
Number of pages	12
Journal	Physica D: Nonlinear Phenomena
Volume	76
Issue number	1-3
DOIs	https://doi.org/10.1016/0167-2789(94)90247-X
State	Published - 1 Sep 1994

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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abstract = "Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrible cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.",

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AB - Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrible cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.

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Passive scalars and three-dimensional Liouvillian maps

Abstract

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