1 SHORT WAVE INSTABILITIES OF COUNTER-ROTATING BATCHELOR VORTEX PAIRS

Recently, investigations have considered the cooperative elliptic instability which forms by the mutual co-existence of a counter-rotating Batchelor-type vortex pair. Such vortex pairs are observed in the wake of an aircraft and pose a significant danger to trailing aircraft. An aircraft flying through the wake of a lead aircraft can exhibit significant loss of lift and control forces; several accidents and near-misses have been recorded. Our investigation has identified that short-wave Kelvin-type instabilities may prematurely destroy the vortex pair. By inducing short-wave instabilities there is the potential to significantly improve safety in the aviation industry. The work has relied heavily on CFD to validate analytical estimates and provide data for future experimental investigations. NOMENCLATURE a characteristic vortex core radius a0 initial characteristic vortex core radius b vortex separation distance k axial wavenumber q swirl number r radial dimension t time t * time coefficient tc characteristic growth time uq azimuthal velocity component z axial dimension Re Reynolds number U self advection velocity W axial velocity component W0 axial velocity coefficient l axial wave length q azimuthal dimension G circulation r density s instability growth rate n kinematic viscosity s * normalized instability growth rate e0 external strain rate w0 vorticit