Passive Scalars and Three-Dimensional Liouvillian Maps

Details Passive Scalars and Three-Dimensional Liouvillian Maps Passive Scalars and Three-Dimensional Liouvillian Maps

1994-10-21

arxiv.org/abs/chao-dyn/9410005v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, plain TeX, appears in Physica D, 76, 22-33, 1994. The figures are available from the authors on request

Scientific paper

10.1016/0167-2789(94)90247-X

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-integrable 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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