Three-dimensional stability analyses of intense atmospheric vortices with secondary circulations

The classical approach of analyzing linearized dynamics of small perturbations to vortices has yielded substantial insight into the behavior of intense atmospheric vortices, helping to explain such phenomen as multiple vortex formation in tornadoes and rapid inner-core structure change in hurricanes. The vast majority of these studies, however, have been applied to essentially two dimensional perturbations to two-dimensional vortices. In some studies, three dimensional perturbations have been considered, but the basic-state vortices were homogenous in the vertical direction.

Intense atmospheric vortices of all types are not homogenous along their vertical axis, but rather have considerable variation of their wind and density fields with height. Furthermore, their interaction with the surface leads to the development of a swirling boundary layer which gives rise, especially in the cases of tornadoes and hurricanes, to a substantial secondary circulation which plays a crucial role in the formation and maintenance of the inner core structure of the vortex. With these facts in mind, we have developed a methodology that allows for the linearized stability analysis of truly three dimensional (but axisymmetric) intense atmospheric vortices with realistic wind and density profiles. The methodology also allows for the inclusion of the secondary circulation. We will present the results of stability analyses of idealized hurricanes, hurricane wind fields generated from mesoscale models, and tornado-like wind fields generated from simple numerical models.