Abstract/Summary

Convection schemes are a large source of error in existing climate and weather prediction models, likely because most schemes are not scale aware and because net mass transport by convection and convective memory are usually ignored. A relatively new approach called the multi-fluid method may be able to address this issue by modelling the convective updraft as a separate fluid from the rest of the atmosphere, allowing convective plumes to be modelled prognostically at any resolution. In this thesis, we investigate the properties of multi-fluid systems and create a 2-fluid model for dry convection where the fluids are defined by the sign of the vertical velocity. We derive and analyse 20 numerical schemes for transferring mass between fluids (entrainment and detrainment). Two of these schemes, which transfer the mass and fluid properties implicitly, are accurate, bounded, conserve momentum and do not increase the total energy for any timestep. We also extend the stability analysis of Thuburn et al. (2019), who showed that a Kelvin-Helmholtz-like instability exists in the 2-fluid incompressible equations with a shared pressure. By using a pressure perturbation for each fluid proportional to fluid convergence, we show that the instability is significantly suppressed. Moreover, using transfer terms between fluids which are also proportional to convergence, the instability can be removed. We also analyse a high resolution dry convection test case and show that the convergence-based pressure and transfer assumptions are accurate. By using the transfer scheme and fluid pressure anomaly proportional to velocity divergence, the 2-fluid scheme was able to transport heat more effectively than the single-fluid scheme for multi-column grey-zone resolutions. Some errors remain for the multi-column test cases because parameters were tuned for the singlecolumn set-up, for which the 2-fluid scheme is able to accurately model the dry rising bubble test case.