Organized Convective Systems: Archetypal Dynamical Models, Mass and Momentum Flux Theory, and Parametrization

Abstract

A dynamical basis is established for understanding the structure and transport properties of organized convection and for expediting its parametrization in large‐scale models. A two‐dimensional model provides an exact theory of the momentum transport by mesoscale convective systems and similar phenomena. the system‐scale dynamics are supposed to dominate local processes and are modelled by a stationary triple‐branch airflow regime consisting of a double‐branch updraught and a downdraught. It is argued that a jump updraught is essential and has a fundamental effect on the momentum transport. the triple‐branch model degenerates into a form of conservative density current; another limiting case consists of a propagating positive pressure jump of maximum amplitude‐an overturning updraught but no downdraught. the functional relationship among dynamical parameters is determined by a characteristic regime equation derived from elementary nonlinear Lagrangian conservation properties and the volume integral of the horizontal‐momentum equation. The inflow to the archetypal jump updraught is constant. an example shows that the inclusion of shear in this region alters the detailed shape of the momentum flux profile but its fundamental character, namely the negative values of momentum flux for a system travelling in the positive x‐direction, is retained. This result, together with recent numerical simulations, implies that low‐level shear directly influences the initiation and evolution of convective elements, whereas the mature‐state fluxes for which the system‐scale flow organization and tilt is paramount is a product of the distribution of heat sources/sinks and deep tropospheric shear. the universal nature of the momentum flux profiles is explained in elementary terms by appealing to dynamical theory. The physical basis of the model and the momentum flux profiles are validated by using published results. the archetype emulates the basic character of the mass and momentum fluxes by mesoscale convective systems. For example an upper‐tropospheric flow deceleration is consistent with the observed effect of tropical cloud clusters on the mean flow but is distinct from the balanced response due to diabatic heating. The theory is used to develop a dynamical approach to the parametrization of organized convective processes that have hitherto been neglected in global models. Mass and momentum fluxes are obtained from the archetypal model in an approach that is fundamentally different from the statistical or averaging approximations that characterize present techniques. the activation of the parametrization scheme is also studied. Mass‐flux criteria are used to define an amplitude function for the mesoscale flux divergence to incorporate the flux laws into the large‐scale equations. the work can be extended to include thermodynamic fluxes by using generalized conservation properties.