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

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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 transport, compared to steady-state boundary-layer predictions. Cross-cell mass transport over large horizontal distances in large aspect ratio domains is inhibited by the primary rising and sinking currents, whose positions would vary over a time scale much longer those associated with boundary-layer instabilities. At high Ra, between 107 and 108, we find a total breakdown of globally connected thermal plumes for base-heated convection. In this hard turbulent regime the plumes become disconnected and efficiency in mass transport is enhanced. The efficiency of mixing is not only governed by the magnitude of the convective velocities but also by the style of convection. With internal heating the large-scale flow becomes smaller and mass transport between neighboring cells is increased by the temporal variabilities in the flow patterns induced by internal heating. Mixing in the Earth's mantle is thus influenced by many factors. Among them are the complexity and strength of time-dependent convection, the aspect-ratio of the global configuration and the amount of internal heating.

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