Spatio-temporal development of the long and short-wave vortex-pair instabilities

We consider the spatio-temporal development of the long-wave and short-wave 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 W0/U0 the ratio between the self-induced velocity of the pair and the axial advection velocity. For sufficiently small W0/U0, the instabilities are convective, but an increase of W0/U0 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 farfield wakes of high aspect ratio wings.