Nonhydrostatic barotropic instability: Applicability to nonsupercell tornadogenesis

This paper reports a barotropic instability analysis of nonhydrostatic colu mnar disturbances in a layer of homogeneous fluid over a flat bottom surfac e. The extended form of Hamilton's principle of least action is used to obt ain 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 pa rameters supposedly relevant to an environment of nonsupercell tornadoes (N ST), 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 she ar zone to form strongly unstable gravity-vorticity hybrid modes. Their ins tability properties are by and large compatible with the observed counterpa rts of NST, such as growth rate, phase speed, length scale, aspect ratio, s tructure, and energetics. Those results are robust for a reasonable range o f each key parameter. Apart from a number of caveats, it is reasonable to s uggest that nonhydrostatic barotropic instability is applicable to NST gene sis.