RAYLEIGH-BENARD CONVECTION IN LIMITED DOMAINS: PART 1 - OSCILLATORY FLOW

Abstract

Transition from the steady state to an oscillatory regime in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, has been examined by direct numerical simulation. Two different physical problems have been considered: the first is related to a domain 3.5 x 1 x 2.1 filled with water at 70 degrees C (Prandtl number 2.5); the second considers a domain 2.4 x 1 x 1.2 filled with water at 33 degrees C (Prandtl number 5). The Rayleigh number has been varied from 20,000 to 80,000. A new procedure based on a statistical approach for evaluation of the critical Rayleigh number for transition from steady state to oscillatory flow (RaII) has been introduced in order to reduce numerical errors and estimate the error bars. A systematic study for the determination of RaII has been conducted as a function of the geometries considered and the different flow structures observed.