Intense atmospheric vortices are the central feature of many important weather phenomena, occurring over wide scales from tornadoes to hurricanes to midlatitude cyclones. The interactions of these vortices with the surface (and humanity) is mediated by the swirling boundary layers which develop beneath them. Solutions describing such boundary layers, such as those from Ekman, Eliassen, and Von Karman, provide useful insight into their structure and behavior.

Observational, experimental, and numerical studies have shown that such swirling layers are generally unstable, and will develop quasi-streamwise rolls once they reach a sufficient intensity. These instabilities are studied using a model of linearized dynamics which allows for arbitrary structure of the axisymmetric vortex and its frictionally induced secondary circulation. The linearized model finds instabilities with wavelengths and growth rates in fair agreement with those produced in a nonlinear model. The primary energy source for growth is the vertical shear of the azimuthal wind. Instabilities appear once the low-level flow develops a jet structure caused by radial inflow and the conservation of angular momentum.