A Geometric Model of Balanced, Axisymmetric Flows with Embedded Penetrative Convection

Abstract

A Lagrangian element model is described which represents axisymmetric flow as a set of toroidal elements, each of which is homogeneous in potential temperature and angular momentum. The flow is assumed to be in gradient wind and hydrostatic balance at all times; this requires that all element interfaces satisfy the rotational equivalent of Margules' formula for the slope of a front. For the flow to be convectively and inertially stable, the element geometry can be shown to adopt a unique configuration at any time. This may be precisely expressed as a requirement for a modified pressure function to be convex in a certain mapping of the space coordinates. Impulses of heat are given to groups of elements to simulate the release of latent heat energy during moist convection. The subsequent element configuration represents the balanced equilibrium state resulting from penetrative convection when the azimuthal-mean angular momentum is conserved. The model demonstrates the formation of a low-level warm core cyclone bounded by a frontal surface and an upper-level anticyclonic lens composed of convected elements. It provides a simple picture of the role of convection in explosive cyclogenesis, polar low and hurricane formation, and allows some aspects of the cooperative interaction between synoptic and convective scale to be treated explicitly?without parametrization.