An atmospheric balanced model of an axisymmetric vortex with zero potential vorticity

Abstract

This paper presents an atmospheric axisymmetric balanced model for a zero potential vorticity vortex that is vertically confined between two frictional boundary layers. Zero potential vorticity has the consequence that the potential temperature does not vary on angular momentum surfaces. This leads to neutrality with respect to symmetric instability. The axisymmetric balanced model conserves this flow property when the diabatic heating and the torque also do not vary on angular momentum surfaces. With these conditions and a transformation to the potential radius coordinates, the model reduces to prognostic equations for the physical radii at the lower and upper boundaries. The knowledge of these radii is sufficient to deduce all dynamic fields of the axisymmetric vortex. Analytical solutions can be obtained for vanishing viscosity and a prescribed heating profile. However, these solutions may reveal a frontal collapse in a finite time. This circumstance can be avoided by the inclusion of a horizontal diffusion term within the boundary layers. Then, the model produces a vortex resembling a tropical cyclone for a typical heating profile. It is suggested that the model might be used for a better conceptual understanding of tropical cyclogenesis.