Nonlinear Dynamics: Coherent Structures

We investigate the edge state in the thermal convection with constant temperature gradient in the vertical direction. In this Rayleigh-Bénard convection system, we see the presence of an elevator mode, which corresponds to axially uniform vertical jets, and a stable periodic orbit, which corresponds to a quiescent state. Using edge tracking method, we perform shooting of different initial conditions between the elevator mode and the stable periodic orbit. Our results reveal the existence of tori for this system. In addition, we identify that an unstable torus represents the edge state which forms boundary between the stable periodic orbit and a stable torus. The identification of this torus edge state adds to the repertoire of dynamical systems approach to the transition phenomenon in fluid flow systems.

Funding acknowledgement

AD Mendoza and JRT Lustro are grateful to the COOPERATE Program of the Office of International Linkages of the University of the Philippines for supporting the conduct of this study.