A skirted Rankine combined vortex model

Tangential winds in such atmospheric vortices as dust devils, tornadoes, mesocyclones, water- and landspouts, and tropical cyclones, to a first approximation, may be modeled as a classical Rankine combined vortex (RCV), which consists of a core in solid-body rotation surrounded by a potential vortex where the tangential wind is inversely proportional to radial distance from the center of the vortex. The RCV model produces a top-hat profile of vertical vorticity in the vortex embedded in an irrotational environment (potential vortex). This prediction is very crude owing to (a) the simplicity of the RCV model, and (b) the model's inherent discontinuity in vorticity at the vortex's core radius where a peak tangential wind occurs. The discontinuity cannot be a natural entity for viscous vortex flow.

To eliminate the discontinuity from the RCV model, we have developed an analytical “skirted” RCV model in which the radial profiles of tangential wind and vertical vorticity create (a) a smooth transition between the inner and outer profiles in the annular region of maximum tangential velocity and (b) the nonzero “skirt” of vertical vorticity in this region. The corner portions of the top-hat profile of vertical vorticity become curved. This transition indicates that the turbulent mixing takes place which reduces the cusp in the annular region of maximum tangential velocity. The tangential velocity profiles of dust devils, laboratory-simulated vortices, and tropical cyclones are very good examples of the “skirted” Rankine combined vortex