A GENERAL-THEORY FOR 2-DIMENSIONAL VORTEX INTERACTIONS

A general theory for two-dimensional vortex interactions is developed from the observation that, under slowly changing external influences, an individual vortex evolves through a series of equilibrium states un til such a state proves unstable. Once an unstable equilibrium state i s reached, a relatively fast unsteady evolution ensues, typically invo lving another nearby vortex. During this fast unsteady evolution, a fr action of the original coherent circulation is lost to filamentary deb ris, and, remarkably, the flow reorganizes into a set of quasi-steady stable vortices. The simplifying feature of the proposed theory is its use of adiabatic steadiness and marginal stability to determine the s hapes and separation distance of vortices on the brink of an inelastic interaction. As a result, the parameter space for the inelastic inter action of nearby vortices is greatly reduced. In the case of two vorte x patches, which is the focus of the present work, inelastic interacti ons depend only on a single parameter: the area ratio of the two vorti ces (taking the vorticity magnitude inside each to be equal). Without invoking adiabatic steadiness and marginal stability, one would have t o contend with the additional parameters of vortex separation and shap e, and the latter is actually an infinitude of parameters.