Roles of Streamwise and Transverse Partial-Vorticity Components in Steady Inviscid Isentropic Supercell-Like Flows

Investigations of tornadogenesis in supercells attempt to find the origin of the tornado's large vorticity by determining vorticity generation and amplification along trajectories that enter the tornado from a horizontally uniform unstable environment. Insights into tornadogenesis are provided by finding analytical formulas for vorticity variations along streamlines in idealized, steady, inviscid, isentropic inflows of dry air imported from the environment. The streamlines and vortex lines lie in the stationary isentropic surfaces so the vorticity is 2D. The transverse vorticity component (positive leftward of the streamlines) arises from imported transverse vorticity and from baroclinic vorticity accumulated in streamwise temperature gradients. The streamwise component stems from imported streamwise vorticity, from baroclinic vorticity accrued in transverse temperature gradients, and from positive transverse vorticity that is turned streamwise in cyclonically curved flow by a "river-bend process." It is amplified in subsiding air as it approaches the ground. Streamwise stretching propagates a parcel's streamwise vorticity forward in time. In steady flow, vorticity decomposes into baroclinic vorticity and two barotropic parts vBTIS and vBTIC arising from imported storm-relative streamwise vorticity (directional shear) and storm-relative crosswise vorticity (speed shear), respectively. The Beltrami vorticity vBTIS is purely streamwise. It explains why abundant environmental storm-relative streamwise vorticity close to ground favors tornadic supercells. It flows directly into the updraft base unmodified apart from streamwise stretching, establishing mesocyclonic rotation and strong vortex suction at low altitudes. Increase (decrease) in storm-relative environmental wind speed with height near the ground accelerates (delays) tornadogenesis as positive (negative) vBTIC is turned into streamwise (anti-streamwise) vorticity within cyclonically curved flow around the mesocyclone.