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Multi-fluid models have recently been proposed as an approach to improving the representation of convection in weather and climate models. This is an attractive framework as it is fundamentally dynamical, removing some of the assumptions of mass-flux convection schemes which are invalid at current model resolutions. However, it is still not understood how best to close the multi-fluid equations for atmospheric convection. In this paper we develop a simple two-fluid, single-column model with one rising and one falling fluid. No further modelling of sub-filter variability is included. We then apply this model to Rayleigh-Bénard convection, showing that, with minimal closures, the correct scaling of the heat flux (Nu) is predicted over six orders of magnitude of buoyancy forcing (Ra). This suggests that even a very simple two-fluid model can accurately capture the dominant coherent overturning structures of convection.

Traditional parameterizations of convection are a large source of error in weather and climate prediction models and the assumptions behind them become worse as resolution increases. Multifluid modeling is a promising new method of representing sub- and near-grid-scale convection allowing for net mass transport by convection and non-equilibrium dynamics. The air is partitioned into two or more fluids which may represent, for example, updrafts and the nonupdraft environment. Each fluid has its own velocity, temperature and constituents with separate equations of motion.\ud \ud This paper presents two-fluid Boussinesq equations for representing sub-grid-scale dry convection with sinking and w = 0 air in fluid 0 and rising air in fluid 1. Two vertical slice test cases are developed to tune parameters and to evaluate the two-fluid equations: a buoyant rising bubble and radiative convective equilibrium. These are first simulated at high resolution with a single-fluid model and conditionally averaged based on the sign of the vertical velocity. The test cases are next simulated with the two-fluid model in one column. A model for entrainment and detrainment based on divergence leads to excellent representation of the convective area fraction. Previous multi-fluid modeling of convection has used the same pressure for both fluids. This is shown to be a bad approximation and a model for the pressure difference between the fluids based on divergence is presented.