We use a simple toy model of a downdraft with varying forcing types and a wide variety of vertical wind profiles in order to study this problem. The following key points emerge from our simulations. 1) The mechanism for producing surface vertical vorticity appears to be baroclinic horizontal vorticity generation by the downdraft, with subsequent tilting by the downdraft. Vertical wind shear is not directly required for this process. 2) Experiments with no vertical wind shear, but moderate amounts of downdraft-relative flow, produce substantial surface vertical vorticity. The surface vorticity production is almost zero for no flow, increases monotonically up through downdraft-relative winds of 12.5 m/s, and then falls off monotonically above 12.5 m/s. 3) Although vertical wind shear is not necessary for the downdraft to produce surface vertical vorticity, the simulated patterns of outflow and vortex lines only resemble observations when a typical sheared wind profile is employed.
We conclude that lower tropospheric vertical wind shear may be important to surface vorticity production because it governs the magnitude of the downdraft-relative flow within the supercell, and because it favors the typical configuration of surface outflow and vertical vorticity that can routinely be exploited by the supercell's updraft.