Numerical studies of three-dimensional breakdown in trailing vortex wakes

The development of dangerous vortex wakes trailing between aircraft for appreciable distance downstream, and posing hazards to following aircraft, is calculated using finite-element three-dimensional relaxation methods. Near-wake, middle-wake, and far-wake conditions are delineated. Vortex system finite lifetimes can be calculated with greater facility owing to the inclusion of a self-induction term in the solution dependent upon local curvature and vortex core radius. Looping and convergence phenomena are studied for single vortex pairs, twin pairs, and multiple pairs. Proportions of flap span and wing span are shown to affect the time to convergence of vortex pairs. The self-induction term renders the convergence time of vortices a sensitive function of wavelength. Wakes trailing between wide-body ('Jumbo') aircraft are also examined.