Flow transitions and pattern selection of the rayleigh-bénard problem in rectangular enclosures

In this paper, research efforts in the broad area of flow transitions of Rayleigh-Bénard convection in rectangular enclosures with sidewalls are reviewed. Numerical studies are given primary emphasis. However, experimental works that are relevant are described. Our current physical understanding of the transition phenomena as occurring in the Rayleigh-Bénard problem is critically reviewed. Two broad categories of transition are discussed. In the former, the transitions are temporal in nature, and mostly confined to small enclosures. In the latter, transitions are a result of change in spatial patterns. This phenomenon, known as pattern selection, is looked into for both small and intermediate enclosures.