Does the hook echo instigate tornadogenesis?

The rain curtain associated with the hook-shaped appendage to a radar echo is usually regarded as a passive indicator of a tornado. In this paper I speculate that the hook actually instigates tornadogenesis by two possible mechanisms.

In the first mechanism the tornado derives its spin from vorticity generated baroclinically near the ground. An analytical Lagrangian model is used to show that a straight air current passing through a cool downdraft in an unstably stratified environment acquires significant baroclinic vorticity during descent. Air on the left (right) side of the current exits the downdraft with streamwise (antistreamwise) horizontal and cyclonic (anticyclonic) vertical vorticity. If the air on the left side passes out of the downdraft along the ground into a neighbouring updraft, its cyclonic spin is greatly amplified by vertical stretching of cyclonic vorticity and tilting up of streamwise vorticity.

The second mechanism is modelled using a steady axisymmetric Beltrami flow to describe an updraft that is rotating at mid levels and a surrounding concentric downdraft. Updrafts in helical environments naturally resemble this flow prior to becoming water loaded. It is hypothesized that tornadogenesis is initiated by a rain curtain that forms near the edge of the updraft. In an axisymmetric model the "hook" has to be represented as a concentric rain curtain. The downdraft induced by water loading and evaporative cooling upsets the balance of the Beltrami flow by altering the meridional flow. The downdraft and part of its outflow that moves towards the axis serves to transport high-angular-momentum air downward and inward towards the updraft where it is entrained by the central updraft. It also increases the low-level convergence into the updraft. From a vorticity perspective the baroclinic vorticity is stuck in the azimuthal component as a result of axisymmetry and so the spin-up is a result of upward tilting of inward radial barotropic vorticity and stretching of cyclonic vertical barotropic vorticity. The vortex may build down to the surface via a dynamic pipe effect. Note that in contrast to the first mechanism, the vorticity generated by the hook's negative buoyancy is not the origin of tornadic rotation at the surface.

In nature, hooks are arc-shaped rather than axisymmetric so that a mixture of the effects may occur.