Dynamics of elevated vortices

An account is given of theoretical hydrodynamic models for the behavior of vortices with axially varying rotation rates. For purposes of illustration, two flow classes are considered: radically unbounded solid body-type vortices; and vortex cores of finite radius embedded within radially decaying vortex profiles. For the first type of flows, the von Karman-Bodewadt similarity principle is applied and new exact solutions of the nonlinear Euler equations obtained. For the second class of vortex flows, a linear analysis of the Euler equation is employed. This linear solution describes the formation of a central updraft and an annular downdraft ringing the periphery of the vortex core.