Probabilistic two-phase wake vortex decay and transport model

Abstract

A new parametric wake vortex transport and decay model is proposed that predicts probabilistic wake vortex behavior as a function of aircraft and environmental parameters in real time. The probabilistic two-phase wake vortex decay model (P2P) accounts for the effects of wind, turbulence, stable stratification, and ground proximity. The model equations are derived from the analytical solution of the spatiotemporal circulation evolution of the decaying potential vortex and are adapted to wake vortex behavior as observed in large-eddy simulations. Vortex decay progresses in two phases, a diffusion phase followed by rapid decay. Vortex descent is a nonlinear function of vortex strength. Probabilistic components account for deviations from deterministic vortex behavior inherently caused by the stochastic nature of turbulence, vortex instabilities, and deformations, as well as uncertainties and fluctuations that arise from environmental and aircraft parameters. The output of P2P consists of confidence intervals for vortex position and strength. To assign a defined degree of probability to the predictions reliably, the model design allows for the continuous adjustment of decay parameters and uncertainty allowances, based on a growing amount of data. The application of a deterministic version of P2P to the Memphis wake vortex database yields favorable agreement with measurements.