Stability of symmetric and asymmetric vortices over slender conical wing-body combinations

Theoretical analyses of the stability of symmetric and asymmetric vortex pairs over slender conical wing-body combinations consisting of a slender circular or elliptic cone and a flat-plate delta wing under small perturbations in an inviscid incompressible steady flow at high angles of attack with or without sideslip are presented. The three-dimensional flow problem is reduced to a problem in two dimensions, for which a general stability condition for vortex pairs can be applied. The stationary positions of symmetric and asymmetric vortex pairs and their stabilities are examined for various geometric configurations, angles of attack, and sideslip. Results of the analyses are compared with available experimental data and used to help gain insight into the flow behavior.