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

Using finite-diference discretization procedures, authors explore numerical ly the route to chaos followed by the system when the Rayleigh number Ra in creases. They show that the larger the Rayleigh number is, the more sensiti ve the attractor becomes to time steps and mesh grids. The attractor bifurc ates from a limit point to a limit cycle via an overcritical Hopf bifurcati on 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 attracto r is a limit cycle fit on a two-torus. For Ra = 4.10(6), the attractor appe ars chaotic again. (C) 2001 Editions scientifiques et medicales Elsevier SA S.