Relationship between corotating vortex-pair equilibria and a single vortex in an external deformation field - art. no. 074103

摘要

Two-dimensional corotating vortex pairs are computed as equilibrium solutions of the Euler equations and the influence of one vortex on the other is characterized in terms of a deformation field acting on an isolated vortex region. It is shown, by computing equilibrium states for a single vortex within an equivalent strain field, that the external rotating strain accounts for the elliptic deformation of the streamlines near the center of each vortex. Critical states, as a function of the strain rate, are reached when stagnation points start to penetrate the vortex regions at the outer boundary. While critical states for a single vortex within a uniform external rotating strain field consist of elliptical corner solutions, the vortex shapes lose the elliptical symmetry in the corotating case. We show that these asymmetric equilibrium states can be captured by a single vortex model if we consider higher order terms in the deformation field. We also demonstrate that the critical strain rates are of the same order of magnitude for both the single-vortex model and the interacting vortex pair. (c) 2005 American Institute of Physics.