The Northwest Research Associates (NWRA) Aircraft Vortex Spacing System (AVOSS) Prediction Algorithm computes trailing vortex trajectories and circulation decay in a plane perpendicular to the path of the aircraft that has generated the vortices. Underlying the algorithm are the following assumptions: initial vortex conditions assume that all trailing vorticity due to lift is rolled up into a vortex pair; away from the ground, the vortices are transported laterally at the speed of the local crosswind, and transport due to large-scale turbulence is not included; crosswind shear effects are not included, except as might arise from the previous assumption; and the circulation decay rate for each member of the vortex pair is the same.
For the purpose of the algorithm, the vortices are considered to evolve through four distinct phases. The algorithm treats each of these four phases in a different way, but handles the transitions between phases in a “seamless” manner so that the output of the algorithm makes no distinction between the phases.
Phase I treats the evolution of the vortices away from the ground. Vortex behavior during this phase is described by equations based on those presented by Sarpkaya. Phase 1 is applied only if the wake vortex does not descend close to the ground before demise; i.e., the wake vortex remains above the effect from any ground interaction. Phase II begins when the vortices first start to “feel” the effect of the ground, but are not close enough to the ground to cause the generation of secondary vorticity. Phase III begins when the vortices approach close enough to the ground that their interaction with the ground produces secondary vorticity. Phase IV is an extension of Phase III that corresponds to the continued generation of vorticity at the ground. If the vortices start out close enough to the ground that they immediately should be in Phase II or Phase III, then Phase I is skipped.
Basic assumptions for the four phases are as follows. In Phase I, it is assumed that the evolution of the vortices is influenced by atmospheric stratification, cross wind, and turbulence effects, and can be described by equations based on those presented by Sarpkaya. The atmospheric conditions are represented by vertical profiles of potential temperature, cross wind, and eddy dissipation rate (EDR). The algorithm determines the stratification from the potential temperature profile. At altitudes where the gradient of the temperature is not positive, the stratification is assumed to be neutral.
In Phases II, III, and IV, it is assumed that the evolution of the vortices can be represented by the dynamics of point vortices. In Phase II, it is assumed that the effect of the ground can be represented by image vortices. In Phase III, it is assumed that the effects of ground-generated countersign vorticity can be represented by the introduction of secondary vortices, and in Phase IV, it is assumed that further ground-generated vorticity can be represented by the introduction of additional secondary vortices. Image vortices are also included in Phases III and IV to maintain a zero vertical velocity at the ground. The circulation decay rate obtained by the end of Phase I is assumed to persist throughout Phases II, III, and IV.
For Phase I, the algorithm uses numerical software that solves a system of three ordinary differential equations using a constant time step. For Phases II, III, and IV, the algorithm uses numerical software that adaptively (variable time step) solves systems of ordinary differential equations that govern the motion of mutually interacting point vortices. In the event that the circulation goes to zero in any of the phases, execution of the algorithm continues in order to provide AVOSS with a time at which the vortices exit the flight corridor through the corridor’s lateral boundaries. During this extended portion of the algorithm’s execution, the altitude of the primary vortices is kept constant and their circulation is maintained at zero.