NESTED INVARIANT 3-TORI EMBEDDED IN A SEA OF CHAOS IN A QUASIPERIODIC FLUID FLOW

Autor:	Hope Weiss, Andrew J. Szeri
Rok vydání:	2009
Předmět:	Superposition principle Coincident Applied Mathematics Modeling and Simulation Phase space Quasiperiodic function Mathematical analysis Braid Torus Fixed point Engineering (miscellaneous) Mathematics Hyperbolic equilibrium point
Zdroj:	International Journal of Bifurcation and Chaos. 19:2181-2191
ISSN:	1793-6551 0218-1274
Popis:	Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincaré sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincaré cross-section. This framework has applications to tidal and other mixing problems of geophysical interest.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b0dc1673caa420b47b4dbae0f1f67094 https://doi.org/10.1142/s0218127409024001 Zobrazit plný text záznamu