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 subgrid‐scale and near‐grid‐scale convection allowing for net mass transport by convection and nonequilibrium 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. This paper presents two‐fluid Boussinesq equations for representing subgrid‐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 multifluid 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.

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.

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<p>Atmospheric convection remains one of the weakest parts of weather and climate models, especially in the tropics. As model resolutions increase, the assumptions underlying traditional convection parametrisations break down; however, we are still far from fully resolving all convective processes, showing a need for convection parametrisation well into the future.</p><p>A multi-fluid framework for parametrising convection has been proposed, based on conditionally filtering the Navier-Stokes equations. This results in a set of equations for multiple fluids, where each fluid has its own dynamic and thermodynamic fields. The approach is fully 3D and time-dependent, allowing for both convective memory and net mass transport due to convection. However, the approach differs from higher-order turbulence closures in that it attempts to capture the important coherent structures of convection via the partitioning into multiple fluids. In addition to the usual sub-filter fluxes, the equations contain terms involving the exchange of momentum, entropy, moisture, and tracers between different fluids. The problem of parametrising convection then becomes the problem of parametrising these exchange terms. This means that within this framework the convection is fundamentally a part of the dynamics: there is no separate “convection scheme" which is called by the dynamical core.</p><p>As a first step towards using this framework to parametrise atmospheric convection, we consider a highly simplified model: dry, 2D Rayleigh-Bénard convection in the Boussinesq limit. This model captures the essentials of buoyant convection, with additional symmetry constraints which help with building a parametrisation. In the single-column limit of the single-fluid case, no circulation can exist. This leads to a very poor solution, in particular vastly underestimating the heat transport.</p><p>In a two-fluid model, the separate dynamical fields for each fluid mean that a circulation can exist even at the coarsest resolutions. We show that a simple two-fluid single-column model can capture all the essentials of the horizontally-averaged time-mean high resolution solution, including the buoyancy, vertical velocity, and pressure profiles, as well as much better representation of the heat flux. We explore the consequences of different choices for the parametrisations of the exchange terms, showing that a good representation of volume, momentum, and buoyancy exchange, and of the pressure difference between the fluids, is required. For this simple case, this is achieved entirely without parametrisation of subfilter terms, showing that the multi-fluid approach is capturing the coherent structures of convection well.</p>

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.