Bifurcations in two-dimensional differentially heated cavity

In this work, we propose a numerical analysis of a bidimensional instationary natural convection in a square cavity filled with air and inclined 45 degree versus to horizontal. The vertical walls are subjected to non-uniform temperatures while the horizontal walls are adiabatic. The equations based on the formulation vorticity-stream function are solved using the Alternating Directions Implicit scheme (ADI) and Gauss elimination method. We analyze the influence of Rayleigh number on the roads to chaos borrowed by the natural convection developed in this cavity, and we are looking for stable solutions representing the nonlinear dynamic system. A correlation between the Nusselt number and the Rayleigh number is proposed. We have analyzed the vicinity of the critical point. The transition of the point attractor to another limit cycle attractor is characterized by the Hopf bifurcation