Lifespan of trailing vortices in a turbulent atmosphere

Abstract

The lifespan of aircraft trailing vortices is controlled by a mutual induction instability excited by atmospheric turbulence. The instability itself is well understood. The purpose here is to incorporate the effects of turbulence and thereby predict wake lifespan as a function of meteorological conditions. Eddies of the relevant size are assumed to lie in the Kolmogorov inertial subrange, characterized by an energy dissipation rate e. The appropriate dimensionless measure of turbulence intensity proves to be η = (∈b)1/3/(T/2πb), where T is the circulation around the vortices, and b is their separation. Similarity considerations imply a mean wake lifespan of the form (2ηb2/T)τ(η), where τ is a universal function of η. A statistical definition of lifespan is proposed, and T is computed in the limit of large η, when the vortices are too weak to influence their own deformation. Vortex induction then is included, and τ is computed in the opposite limit of small η by the method of stationary phase. In that limit, vertical currents are the chief excitors of instability. The two asymptotic forms for τ(η) join in a smooth curve in reasonable agreement with the few published data. The paper concludes with a review of a practical method for actively exciting the mutual induction instability. The method would shorten the typical lifespan of a 747 wake by a factor of 3. © 1976 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.