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 vort ices and b their separation, and upon W-0/U-0 the ratio between the self-in duced velocity of the pair and the axial advection velocity. For sufficient ly 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 thre shold, spatial growth rates are larger than those predicted by temporal sta bility theory. Considering aeronautical applications, it is shown that inst abilities of the type considered in this communication cannot become absolu te in farfield wakes of high aspect ratio wings. (C) 2000 American Institut e of Physics. [S1070-6631(00)01705-0].