Updraft Rotation in Supercells: Beyond Tilting of Horizontal Shear Vorticity

It has been known for many decades that updraft-scale vertical vorticity in thunderstorms results from tilting of ambient horizontal shear vorticity by the updraft.  However, as will be demonstrated, this mechanism does not explain vortex formation in the updraft.  For instance, in a unidirectionally-sheared environment, tilting of horizontal vorticity only produces a couplet of vertical shear vorticity (i.e., no curvature of the streamlines) at the flanks of the updraft. This is tied to the fact that the tilting term in the vertical vorticity equation merely describes differential vertical advection of horizontal momentum.  However, vortex formation is an important step in facilitating e.g., off-hodograph propagation and updraft intensification via the perturbation pressure field associated with the vortex.

The problem of how the vortex forms in the updraft is analyzed from an idealized numerical modeling perspective using the Bryan Cloud Model 1 (CM1).  It is shown that the perturbation pressure field at the flanks of the updraft facilitates a conversion from vertical shear vorticity to curvature vorticity in the unidirectionally-sheared case.  This conversion results in the formation of a vortex as diagnosed e.g., by a closed streamline pattern in the storm-relative frame.  Parallels will be drawn to the formation of a toroidal vortex surrounding a buoyant plume.  Also, forward trajectories of parcels within the storm’s mesocyclone will be presented and the tilting and conversion terms will be analyzed from a Lagrangian perspective.