Transitions to chaos in natural convection

Transitions from steady flow to chaotic flow have been studied for two problems fundamental to understanding non-linear phenomena, which arise in thermal convection in many important scientific and technological settings. The two problems are Rayleigh-Benard convection (RBC) and volumetric heating convection (VHC)-the former being comprised of a rectangular cavity with insulated sidewalls, heated at constant uniform temperature along the bottom and cooled at constant uniform temperature along the top, and the latter 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. These systems provide basic models for flows that occur in many diverse areas. For example, the VHC problem represents a fundamental model both of molten corium flow due to decay heat in a core-catcher following a hypothetical reactor meltdown accident and of convective atmospheric flow that results from the volumetric absorption of solar radiation. The two systems were studied via large-scale numerical simulations carried out using new nodal integral method (NIM) codes for time-dependent flows.