Dynamics of Elevated Vortices

Abstract

Abstract Theoretical hydrodynamic models for the behavior of vortices with axially varying rotation rates are presented. The flows are inviscid, axisymmetric, and incompressible. Two flow classes are considered: (i) radially unbounded solid body–type vortices and (ii) vortex cores of finite radius embedded within radially decaying vortex profiles. For radially unbounded solid body–type vortices with axially varying rotation rates, the von Karman–Bodewadt similarity principle is applicable and leads to exact nonlinear solutions of the Euler equations. A vortex overlying nonrotating fluid, a vortex overlying a vortex of different strength, and more generally, a vortex with N horizontal layers of different rotation rate are considered. These vortices cannot exist in a steady state because continuity of pressure across the horizontal interface between the vortex layers demands that a secondary (meridional) circulation be generated. These similarity solutions are characterized by radial and azimuthal velocity ...