Transitional dynamics in thermal convection between rigid plates

The Rayleigh-Benard thermal convection problem is an instability of a Boussinesq fluid layer on an infinite horizontal plane heated from below and cooled from above in the presence of gravity in the vertical, pointing downward. The dynamics of this phenomena is governed by Boussinesq equations. In this work, Boussinesq equations are integrated numerically using a spectral element technique. The resulting numerical database is then used to generate the Karhunen-Loeve (K-L) basis. The K-L basis is an empirical basis in nature that can be computed from an experimentally or numerically generated database representative of the underlying physical phenomena. The K-L basis is, in turn, used to study the dynamics in the transitional regimes of thermal convection as a preliminary effort prior to extracting a low-dimensional description of the phenomena