Mass and heat transport in strongly time-dependent thermal convection at infinite prandtl number

Abstract

Abstract We have studied heat and mass transport in two-dimensional, infinite Prandtl number, incompressible thermal convection for a range of Rayleigh numbers (Ra), between 106 and 108, and two different aspect-ratio boxes, between 1·8 and 10. This study has been motivated by recent developments in studying the transition from weak to strong turbulence in thermal convection. We have employed a two-dimensional finite element method in solving the time-dependent convection equations. Passive tracers, up to 900, have been put into the flow fields for monitoring the style and pattern of mass transport. At Ra around 106 convection does not take place in a strictly cellular mode. Thermals are ejected from the hot and cold boundary layers. These boundary-layer instabilities enhance the mass transport in the interior of individual cells. The fate of these instabilities is determined ultimately by the large-scale circulation. The persistent large-scale circulation gives rise to a significant decrease of the heat ...