Short-scale instabilities in trailing wake vortices in a stratified fluid

Measurements of the evolution of wingtip trailing wake vortices in nonturbulent and unsheared density-stratified fluids are reported, using both laboratory experiments and a three-dimensional numerical code. As is widely known, and as our laboratory and numerical results confirm, the primary instability for these vortices in an unstratified fluid is the Crow instability, which has a characteristic initial wavelength of around 8.6b(0), where b(0) is the initial separation distance between the vortices. In stratified fluids, however, our laboratory observations and numerical simulations show an instability with a shorter wavelength of around b(0)-2b(0). This instability appears at a time in the evolution when the vertical migration of the vortices has reached nearly its maximum extent. The observed instability grows both in amplitude and wavelength with time. When the vortex Froude number is around one, the instability first becomes visible at a nondimensional time T of around 2 and reaches a maximum at T of around 4. For a commercial aircraft, the latter time corresponds to distances of around 10-25 km behind the aircraft. In flight, at T similar to 4, the vertical peak-to-peak amplitude oscillation of the vortex cores due to this instability could be up to 20 m with a horizontal wavelength around 100 m.