Spatio-temporal Development of the Long and Short-wave Vortex-pair Instabilities Typeset Using Revt E X

We consider the spatio-temporal development of the long-wave and shortwave instabilities in a pair of counter-rotating vortices in the presence of a uniform axial advection velocity. The stability properties depend upon the aspect ratio a=b of the vortex pair, where a is the core radius of the vortices and b their separation, and upon W 0 =U 0 the ratio between the self-induced velocity of the pair and the axial advection velocity. For suuciently small W 0 =U 0 , the instabilities are convective, but an increase of W 0 =U 0 may lead to an absolute instability. Near the absolute instability threshold, spatial growth rates are larger than those predicted by temporal stability theory. Considering aeronautical applications, it is shown that instabilities of the type considered in this communication cannot become absolute in farreld wakes of high aspect ratio wings.