Different modes of Rayleigh-Benard instability in two- and three-dimensional rectangular enclosures

The article describes a complete numerical solution of a recently formulate d benchmark problem devoted to the parametric study of Rayleigh-Benard inst ability in rectangular two- and three-dimensional boxes. The solution is ca rried out by the spectral Galerkin method with globally defined, three-dime nsional, divergent-free basis functions, which satisfy all boundary conditi ons. The general description of these three-dimensional basis functions, wh ich can be used for a rather wide spectrum of problems, is presented. The r esults of the parametric calculations are presented as neutral curves showi ng the dependence of the critical Rayleigh number on the aspect ratio of th e cavity. The neutral curves consist of several continuous branches, which belong to different modes of the most dangerous perturbation. The patterns of different perturbations are also reported. The results obtained lead Co some new conclusions about the patterns of the most dangerous perturbations and about the similarities between two- and three-dimensional models. Same extensions of the considered benchmark problem are discussed. (C) 1999 Aca demic Press.