Velocity and Vorticity Decay in Idealized Axisymmetric Vortical Flows

We explore the rates of decay in the tangential velocity and axial vorticity in various idealized axisymmetric vortical flows that include bathtub vortices, vortex chamber vortices, dust devils, supercell tornadoes, mesocyclones, and tropical cyclones. These all exhibit a common power law, where the velocity decays like r^-β for some 0<β<1. We review the empirical evidence for such a law, provide results from a simple numerical simulation, and provide an analytical model extending Serrin's swirling vortex model to include the r^-β.