A two‐fluid single‐column model of turbulent shallow convection. Part II: Single‐column model formulation and numerics

The two-fluid single-column model of thuburn et al. (2019) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy introduced as a prognostic variable, dependence on diagnosed boundary layer height removed, subfilter fluxes are approximated using version Mellor-Yamada scheme. Three mechanisms for entrainment detrainment processes introduced, which represent unstable air at the surface, forced top boundary/cloud layers, turbulent mixing relaxes convective fluid reference profile. A semi-implicit Eulerian discretization replaces semi-Lagrangian implementation improve numerical stability conservation. equations implicit time step solved quasi-Newton method, shown perform well in tests conservation convergence. presented this article will be applied simulations shallow cumulus convection Part III.