Numerical study of two-dimensional transient natural convection in an air filled square enclosure, tilted in relation to the horizontal plane, heated from two opposite sides.

Using finite-diference discretization procedures, authors explore numerically the route to chaos followed by the system when the Rayleigh number Ra increases. They show that the larger the Rayleigh number is, the more sensitive the attractor becomes to time steps and mesh grids. The attractor bifurcates from a limit point to a limit cycle via an overcritical Hopf bifurcation for a Rayleigh number value between 1.11.10(5) and 1.12.10(5). When the Rayleigh number is increased again, six period-doublings are observed. The attractor comes out chaotic for Ra = 1.13.10(6). For 2.45.10(6), a laminar flow appears and persists until 3.9.10(6). Inside this window, the attractor is a limit cycle fit on a two-torus. For Ra = 4.10(6), the attractor appears chaotic again. (C) 2001 Editions scientifiques et medicales Elsevier SAS.