Since the early work of Fujita, the multiple vortex phenomenon in tornadoes has been widely believed to be caused by dynamic instability of the azimuthal and vertical wind profiles as a function of radius from the vortex center. However, there is ample observational and numerical evidence that these profiles vary substantially with height, and that embedded within the rotational flow is a significant secondary circulation, with radial inflow at low levels and vertical flow up the vortex axis. This axial flow sometimes supports a "vortex breakdown," below which the flow has a laminar appearance, and above which there are large turbulent motions.

We further investigate these dynamics by extending vortex stability analysis in two ways: first, arbitrary variation with height is allowed for both the basic state and the associated eigenfunctions. Second, the secondary circulation is also included in the basic state. For simple tornado-like vortices generated from an axisymmetric model, unstable modes are shown to be localized just above the point of vortex expanion, as in a "drowned vortex jump." Instabilities in vortices with various profiles, and their dynamic mechanisms, will be presented.