Nonhydrostatic Barotropic Instability: Applicability to Nonsupercell Tornadogenesis

Abstract

This paper reports a barotropic instability analysis of nonhydrostatic columnar disturbances in a layer of homogeneous fluid over a flat bottom surface. The extended form of Hamilton's principle of least action is used to obtain the canonical form of Green?Naghdi equations for this model. The basic state has a monotonic shear flow and a variable depth. For values of the parameters supposedly relevant to an environment of nonsupercell tornadoes (NST), the nonhydrostatic effect is found to have significant impacts. It is capable of sufficiently slowing down some short gravity waves so that they resonantly interact with vorticity waves of the same wavelengths in the shear zone to form strongly unstable gravity?vorticity hybrid modes. Their instability properties are by and large compatible with the observed counterparts of NST, such as growth rate, phase speed, length scale, aspect ratio, structure, and energetics. Those results are robust for a reasonable range of each key parameter. Apart from a number of caveats, it is reasonable to suggest that nonhydrostatic barotropic instability is applicable to NST genesis.