Competition between temporal and spatial transitions are investigated for a model of Bénard convection in thin, horizontal annuli of finite length. The governing system is approximated by six ordinary differential equations, which allow axially-uniform states, governed by the Lorenz equations, as well as axially-periodic ones. When the annulus length is large, axially-periodic structures preempt the one-dimensional flows and any purely temporal instability that might occur. When the length is small, only Lorenz dynamics survive and temporal transitions preempt any spatial ones. At intermediate lengths the two types of transitions compete. All the above can occur in parameter ranges that are physically accessible. Computed Poincaré maps and asymptotic analysis at codimension-two bifurcations exhibit stable two-tori, indicating apossile three-frequency route to chaos. Certain interesting features outside the range of physical validity are investigated for their interest in the theory of dynamical systems.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics