Rayleigh-Benard Convection in a Hele-Shaw Cell: A Numerical Study

摘要

Using a simplified form of the Boussinesq equations and a finite difference scheme the free convective flow in a Hele-Shaw cell of small aspect ratio h/b = 3.5 was calculated. The calculations result in realistic values for the critical Rayleigh numbers for the onset of steady and oscillatory convection. Most of the observed unsteady flow patterns can be simulated numerically. It is shown that five different stable flow patterns can occur at one particular Rayleigh number. The different stable flow patterns are coupled by a variety of complex transitions. The calculations show that a realistic description of the observed flow phenomena can not be obtained by a simplified model using the Darcy law in the momentum equation and implying slip flow at the small confining boundaries.