Bifurcations and unfoldings in natural convection

Extensive numerical studies of bifurcations and unfoldings have been carried out for two important problems in natural convection. These are (a) the Rayleigh-Benard convection (RBC) problem-a rectangular cavity, with insulated sidewalls, heated at constant uniform temperature along the bottom and cooled at constant uniform temperature along the top; and (b) the volumetric heating convection (VHC) problem - a rectangular cavity, with insulated sidewalls and bottom, heated by a constant uniform volumetric heat source and cooled at constant uniform temperature along the top. The information available in the literature on RBC was used to evaluate and justify the approximations made in the current research, which has shed additional light on nonlinear phenomena in RBC and led to new basic information on the bifurcations and unfoldings that occur in VHC for which there were essentially no previous results available. Both problems arise in many important technological and scientific contexts, including reactor safety analysis and meteorological phenomena. In particular, VHC is relevant to the development of an understanding of the natural convective motion driven by the radioactive decay heat in the molten core mixture (corium) in the core catcher following a hypothetical reactor core meltdown accident and of that which occurs in themore » atmosphere due to the deposition of radiant solar energy. The calculations were done using newly developed versions of the nodal integral method (NIM) for steady-state flows in conjunction with extended system methods for numerical bifurcation analysis for the saddle-node and pitchfork bifurcation computations.« less