On Inertial Instability as Related to, the Multiple-Vortex Phenomenon

Abstract

The occurrence of subsidiary vortices (multiple vortices) in intense tornadoes is hypothesized as being due to the development of an inertial instability in a two-celled vortex. The instability is taken to develop within a cylindrical shear layer surrounding a central stagnant subcore. The possible validity of this hypothesis is examined by means of a simple linear stability analysis. The special case of the stability of a rotating flow within strongly sheared azimuthal velocity to non-axisymmetric (cylinder symmetric) disturbances is solved in detail. It is found that the results of this highly simplified vortex model show good qualitative agreement with actual observations. The observed sequence of destabilization of progressively higher wavenumber modes, the shifting of the most unstable mode to large wavenumbers, and the hysteresis effects found in laboratory simulations can all be argued from the model. The results are shown to reduce to the corresponding classical findings of Rayleigh in the appropriate co-limits of small curvature and/or large wavenumber. Streamline patterns for two critical neutral modes are presented and discussed.