NEW CHAOTIC SYSTEM ARISING FROM NON-DARCY RAYLEIGH–BÉNARD THERMAL CONVECTION
by
F.Talay Akyildiz
Ondokuz Mayis University, Arts and Science Faculty, Department of Mathematics, 55139, Samsun, Turkey

The onset of chaotic motion in Newtonian fluid is explored in the context of the Non-Darcy Rayleigh–Bénard thermal convection setup. Galerkin truncation is used to derive a low-order dynamical system from the governing equations which reduces to the classical Lorenz system for the Rayleigh–Bénard thermal convection. The existence of Si’lnikov homoclinic orbits in this system has been proven by using the undetermined coefficient method. As a result, the Si’lnikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of attractors are determined by these homoclinic orbits.

Date received: March 13, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caun-02.