Absolute/Convective Instabilities and Spatial Growth in a Vortex Pair

Abstract

Airplane trailing vortices have a destabilizing effect on ensuing aircrafts. Security spacings,related to the trailing vortices “lifetime” are actually enforced between take-offs and landings. This spacing limits the maximum take-o. and landing frequency in saturated airports [19]. A number of studies have been devoted to the understanding of vortex wake dynamics,usually modeled by a pair of counterrotating vortices. Two types of vortex pair three-dimensional instabilities have been identified in the past: a long-wave instability (of the order of the spacing b between the two vortices) and a short-wave instability (of the order of the vortex core radius a) have been first considered respectively by Crow [1] and by Moore & Saffman [15] and Tsai & Widnall [20]. These two mechanisms,whic h are thought to participate in the vortex wake dissipation,ha ve been observed in recent experiments [12]. One possible technique to accelerate the dissipation of aircraft wakes is to force these instabilities by on-board control devices [2,21,22]. Until now only temporal vortex pair instability analyses are available. If one wants to force these instabilities,ho wever,it would be more appropriate to analyze their spatial stability in the airplane reference frame. As the spatial analysis makes sense only when the instabilities are convective,an absolute/convective stability analysis is required. The results presented consist of the absolute/convective and spatial stability analyses of both long- and short-wave instabilities.