Representing small-scale mixing in a parcel-based geophysical fluid dynamics model

The Elliptical Parcel-in-Cell (EPIC) model is a new approach to geophysical fluid dynamics based around Lagrangian parcels. Parcels in EPIC represent both the thermodynamic and the dynamical prognostic properties of the flow, and the deformation of the parcels is explicitly calculated. We have been testing this approach to study density currents, Rayleigh-Taylor instability, warm/moist bubbles and boundary layers. EPIC provides a high effective resolution compared to fully gridded models.

The Lagrangian approach implies mixing between parcels is explicitly controlled (no numerical mixing). However, mixing between parcels needs to be represented to accurately model, for example, clouds. By default, mixing is modelled as the splitting of elongated (stretched) parcels and the merging of small parcels. Convergence studies show that mixing between parcels is relatively weak at coarse resolution in EPIC, and a high resolution is needed to capture all the relevant turbulent scales.

Modifications to EPIC are made to represent the effects of mixing by eddies that are not resolved by the gridded velocity field used to advect and deform parcels. The modifications are inspired by subgrid formulations in Large Eddy Simulation models, and are designed to ensure conservation laws are respected. We test the effect of these modifications in both idealised studies of warm and moist bubbles and in a more realistic tradewind cumulus case study. Although the modifications can reduce the issue of weak mixing at coarse resolution, they also lead to the suppression of fine-scale circulations when applied to the vorticity field. The modifications result in significant changes to cloud cover, liquid water path distribution, and cloud updraught mass-flux, and make EPIC behave more similarly to an LES with a similar subgrid model.