Passive Scalars and Three-Dimensional Liouvillian Maps
chao-dyn
2012-08-02 v2 Dynamical Systems
Chaotic Dynamics
Fluid Dynamics
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-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.
Cite
@article{arxiv.chao-dyn/9410005,
title = {Passive Scalars and Three-Dimensional Liouvillian Maps},
author = {Julyan H. E. Cartwright and Mario Feingold and Oreste Piro},
journal= {arXiv preprint arXiv:chao-dyn/9410005},
year = {2012}
}
Comments
18 pages, plain TeX, appears in Physica D, 76, 22-33, 1994. (Lack of figures in original submission corrected in this new upload.)