Stability of a four-vortex aircraft wake model

The stability of an aircraft wake model composed of an external vortex pair (modeling the wing tip vortices) and an internal vortex pair rotating in t he opposite direction (modeling the vortices generated by the fuselage and the horizontal tail) in a stationary configuration is investigated with the vortex filament stability method used by Crow [AIAA J. 8, 2172 (1970)] and Crouch [J. Fluid Mech. 350, 311 (1997)]. It is shown that this configurati on is unstable with respect to two-dimensional and three-dimensional distur bances. For long wavelength three-dimensional symmetric perturbations, the rapid growth observed in the numerical simulations of Rennich and Lele [J. Air. 36, 398 (1999)] is found. Moreover, the analysis allows one to show th at without an excitation of the long-wave mode, the system will naturally d evelop short wavelength instabilities localized within the inner vortices w hich do not affect the outer vortices. Inspection of the initial value prob lem shows that the long-wave modes can be efficiently initiated by the intr oduction of perturbations on the internal vortices. (C) 2000 American Insti tute of Physics. [S1070-6631(00)00710-8].