Observables for anticipating tornadogenesis in mesocyclones

We seek to identify an observable for anticipating tornadogenesis in mesocyclones, because such tornadoes are characterized by particularly long life, long and wide path, and high wind speed. We associate tornadogenesis with the transition from a one-cell vortex to a two-cell vortex. In such a transition, 'insertion' of a virtually nonrotating, slowly recirculating core displaces that high-swirl-speed air which is rapidly ascending along a moist-adiabatic locus of thermodynamic states, to an annulus at small but finite distance from the axis of rotation. Such a transition, on a vastly larger lateral scale, is known to characterize intensification of a tropical storm to a typhoon. We examine analytically a quasisteady axisymmetric model of a four-part vortex structure consisting of a bulk potential vortex, near-ground inflow layer, 'eyewall', and 'eye'. We inquire whether such a four-part intense vortex, formed in convectively unstably stratified air, is self-sustaining. In particular, we inquire whether the vertical profile of the angular momentum at the periphery is a discriminant for identifying self-sustaining vortices.