Coexisting attractors in compressible Rayleigh-Bénard flow

Abstract

We demonstrate that precise solutions of the convective flow equations for a compressible conducting viscous fluid can give degenerate stationary states. That is, two or more completely different stable flows can result for fixed stationary boundary conditions. We characterize these complex flows with finite-difference, smooth-particle methods, and high-order implicit methods. The fluids treated here are viscous conducting gases, enclosed by thermal boundaries in a gravitational field{emdash}the {open_quotes}Rayleigh-B{acute e}nard problem.{close_quotes} Degenerate solutions occur in both two- and three-dimensional simulations. This coexistence of solutions is a macroscopic manifestation of the strange attractors seen in atomistic systems far from equilibrium. {copyright} {ital 1997} {ital The American Physical Society}