The Dynamics of Eye Formation and Maintenance in Axisymmetric Diabatic Vortices

Abstract

This paper investigates the occurrence, formation, and maintenance of eyes in idealized axisymmetric balanced vortices with diabatic forcing. Two key elements of the model setup are temperature relaxation toward a specified equilibrium temperature Te and Ekman pumping from a turbulent boundary layer. Furthermore, the flow is assumed to be almost inviscid in the interior. The model does not attempt any closure for moist convection. Previous work by the authors has shown that there is a continuous transition from monsoonlike vortices to hurricane-like vortices. This transition is governed by the ratio F = αT /cD, where αT is the thermal relaxation rate and cD the surface drag coefficient. An eye is defined in terms of the vertical wind with maximum upwelling occurring at some finite radius rather than at the origin. It is possible to obtain an eye even though Te maximizes at the origin, that is, even though Te does not directly predispose upwelling at some finite radius. The occurrence of an eye is controlled by F, and the transition between vortices without any eye and vortices with a clearly defined eye is rather sudden. These results are robust with respect to the amplitude of the forcing or the specific shape of Te. The key role of F is corroborated through a systematic nondimensionalization. In a steady-state hurricane-like vortex, mechanical forcing from Ekman pumping maximizes at some finite radius and is instrumental for the maintenance of an eyelike secondary circulation. On the other hand, eye formation during spinup is a purely inviscid process. The results imply that eye formation is a robust and general feature in vortices with strong diabatic forcing.