Can the hook echo instigate tornadogenesis barotropically?

The rain curtain associated with the hook-shaped appendage to a radar echo is usually regarded as a passive indicator of a tornado, not the instigator of it. Close-range observations made during and subsequent to VORTEX have revealed a hook preceding tornadogenesis in every case, but have not found rain-cooled air at the surface within several kilometers of several strong and violent tornadoes.

A simple incompressible constant-viscosity axisymmetric numerical model of a mesocyclone has been built to find an explanation for these intriguing, but puzzling observations. The environment is neutrally stratified to eliminate potential-temperature perturbations and associated buoyancy forces, and to avoid gravity waves and recirculation of thermal anomalies. The environmental hodograph curve is assumed tacitly to be a clockwise-turning circle, although the environmental winds are not represented explicitly in the model. The initial condition is a Beltrami flow describing an updraft that is rotating cyclonically at mid levels around a low-pressure center surrounded by a concentric downdraft that is anticyclonic (but still consisting of air with positive angular momentum). A convective cell in the helical environment would naturally resemble this Beltrami flow prior to becoming water loaded. The domain is closed to avoid artificial isolation of the updraft from its compensating downdraft. The boundary conditions are no slip on the tangential wind, free slip on the radial and vertical wind to allow strong interaction of a vortex with the ground and to accomodate the Beltrami flow. The unperturbed Beltrami flow decays slowly in amplitude while maintaining its pattern.

Hydrometeors are released through the top above the updraft and fall to the ground near the updraft-downdraft interface in an annular curtain. The downdraft enhancement induced by the precipitation drag upsets the balance of the Beltrami flow by altering the meridional flow. The downdraft and the inward-directed part of its outflow increase low-level convergence beneath the updraft and transport high-angular-momentum air downward and inward towards the axis where it is entrained and stretched by the updraft. From a vorticity perspective, the drag-generated baroclinic vorticity is stuck in the azimuthal component owing to axisymmetry. Spin-up results from tilting of inward radial barotropic vorticity and stretching of cyclonic vertical barotropic vorticity. The resulting "tornado cyclone" has a corner region with an intense axial jet and low pressure capped by a vortex breakdown. Winds in the vortex easily exceed the speed limit for the model. The vortex is surrounded by a weakly anticyclonic, subsiding clear slot and a surface-based ring of divergence. In response to a downward axial pressure-gradient force, the top of the updraft descends, perhaps spelling the ultimate demise of the vortex.

Global budgets indicate that a small conversion of potential energy associated with the descent of liquid water to kinetic energy (KE) alters the flow from a harmless mesocyclone aloft to a tornado cyclone on the ground. The "altered state" has less vertical KE and helicity, more horizontal KE, enstrophy and diffusion.