AbstractA two-dimensional vortex particle model is used for studying the development of the vortex wake generated by the wing of an aircraft in the Trefftz plane. Two-dimensional, finite-area vortex structures simulate the initial vorticity distribution at a near-field cross-section of the wing, as provided by either measurements or simulations. The code is used for studying the effect of weak or strong counter-rotating vortices on the development of an aircraft wake. Application in a three-vortex configuration, consisting of the tip and flap vortices, plus a weak negative vorticity sheet lying between them, supports the hypothesis of Graham that the merging of the tip and flap vortices is prevented, because in such an arrangement the counter-rotating vorticity sheet is wrapped around the primary vortices. The present results indicate that even in the far field the tip and flap vortices remain distinct and follow a helical trajectory with large-pitch and small-radius. The code is next applied to the two-vortex system of Savas’s triangular wing, in which the circulation of the flap vortex is comparable to that of the tip. Although a 2D analysis is inappropriate for stability analysis it is still useful for a quick qualitative investigation. Results indicate that the flap and tip vortices follow a helical trajectory with large-pitch but also very large radius. During one period, the flap vortex covers a span wise distance equal to the wing span. Such a flow has not been observed in flight or in laboratory tests. Actually, Ortegaet al, who studied experimentally the triangular wing of O. Savas, found out that before concluding one full spiral, the vortices are literally destroyed (rapid spreading of their vorticity) by an instability mechanism.
Violent and slow relaxations to sinh‐Poisson equilibrium state in two‐dimensional point vortex system