Barotropic Instability in a Tornado Vortex

Abstract

The barotropic instability of a tornado described by Hoecker is investigated. It is found that wavenumbers of the order of 1 to 5 are significantly unstable, with growth rates of the order of 0.1 to 0.5 s?1, yielding e-folding times small compared to tornado lifetimes. The instability is related to departures from the wind distribution of a combined Rankine vortex. Small departures can yield significant growth rates. Also investigated is the barotropic instability of an idealized vortex with a core of constant angular velocity and constant vorticity surrounded by a belt with twice the core vorticity, extending out to the wind maximum, beyond which the vorticity vanishes. Growth rates of the order of 0.1 s?1 are found at wavenumbers between 3.6 and 4.0, with negligible growth rates outside this region. It is suggested that the instability may lead ultimately to the ?suction vortices? described by Fujita in connection with tornadoes and dust devils.