A Linear Analysis of the Multiple Vortex Phenomenon in Simulated Tornadoes

Abstract

A simple vertically-integrated axisymmetric model is used to Calculate axisymmetric flows for different swirl ratios(s) in tornado simulators. Thew axisymmetric states are then tested for stability using a primitive-equation linear model where the waves have both an azimuthal and a vertical wavenumber. For S high enough for there to be a central downdraft in the axisymmetric vortex, the vortex is unstable; otherwise it is stable. For relatively lows only azimuthal waves 1 and 2 are unstable, with wave 1 most unstable at lows followed by 2 at somewhat highers As S is further increased, the most unstable wave shifts to 4, then 5, and so forth. With some tuning, the model predicts the transitions from 0?1 and 1?2 secondary vortices to occur at about the observed value ofs Vertical wavelength are about 3 m, but they increase with increases There are two modes of instability: one in which only waves 1 or 2 are unstable and which appears at lows and a second mode where waves 4, 5 or 6 are most unstable and which appears at highs These two modes am distinguished mostly by their energetics. Mode 1 receives most of its energy from the radial shear of the vertical wind, while mode 2 receives most of its energy from the radial shear of the tangential wind. In mode 1, all the amplitude of the horizontal streamfunction is contained inside the tangential wind maximum, while in mode 2 much of the amplitude is outside the tangential wind maximum.