Rayleigh-Bénard convection in an intermediate-aspect-ratio rectangular container

Abstract

We report a study of the flow patterns associated with Rayleigh—Bénard convection in rectangular containers of approximate proportions 10 × 5 × 1 at Prandtl numbers σ between 2 and 20. The flow is studied at Rayleigh numbers ranging from the onset of convective flow to the onset of time dependence; Nusselt-number measurements are also presented. The results are discussed in the content of the theory for the stability of a laterally infinite system of parallel rolls. We observed transitions between time-independent flow patterns which depend on roll wavenumber, Rayleigh number and Prandtl number in a manner that is reasonably well described by this theory. For σ [lsim ] 10, the skewed-varicose instability (which leads directly to time dependence in much larger containers) is found to initiate transitions between time-independent patterns. We are then able to study the approach to time dependence in a regime of larger Rayleigh number where the instabilities in the flow are found to have an intrinsic time dependence. In this regime, the onset of time dependence appears to be explained by the recent predictions of Bolton, Busse & Clever for a new set of time-dependent instabilities.