Aircraft Wake–Vortex Evolution in Ground Proximity: Analysis and Parameterization Frank Holzäpfel * and Meiko Steen † DLR, German Aerospace Research Center, Oberpfaffenhofen, 82234 Weßling, Germany DOI: 10.2514/1.23917 Field measurement data of 288 wake–vortex pairs and respective environmental conditions acquired at Frankfurt Airport by means of light detection and ranging, sound detection and ranging/radio acoustic sounding system, and ultrasonic anemometer are used to analyze wake–vortex behavior in ground proximity. Exceptional cases with strong rebounds caused by detached shear layers and obstacles are introduced and estimates of the time needed to clear the runway from wake vortices by advection are provided. The impact of turbulence and crosswind on wake– vortex decay proves to be weak, whereas already light crosswind turns out to be sufficient to cause pronounced asymmetric rebound characteristics. Based on the analyses vortex decay and rebound characteristics are parameterized and implemented into the probabilistic two-phase aircraft wake–vortex model. Deterministic and probabilistic prediction skill of the enhanced vortex model are assessed. Comparison to wake predictions out of ground effect indicates that in ground effect 1) the rapid-decay phase progresses slower, 2) wake–vortex evolution can be predicted with improved accuracy, and 3) fair prediction skill requires only limited environmental data. Nomenclature A = constant b = vortex spacing C = constant to adjust turbulent spreading q = rms turbulence velocity R = mean radius T = parameter for vortex age t = time u = axial velocity v = lateral velocity w = descent speed y = spanwise coordinate, positive for port vortex z = vertical coordinate, positive pointing upwards  = circulation  = eddy dissipation rate  = standard deviation  = (effective) kinematic viscosity Subscript g = minimum height above ground l = lower limit lat = lateral meas = measured prim = primary sec = secondary u = upper limit vert = vertical 0 = initial value 00 = value at minimum height 1 = first decay phase 2 = second decay phase 5–15 = 5 to 15 m average Superscript * = normalized by initial vortex parameters b 0 , t 0 , w 0 ,  0 b = normalized by probabilistic bounds I. Introduction P ERSISTENT aircraft trailing vortices entail aircraft separation distances that degrade aviation efficiency at busy airports. Because of comprehensive research efforts on both sides of the Atlantic, wake–vortex advisory systems that aim to safely adjust aircraft separations based on wake–vortex behavior prediction and monitoring seem to come into reach [1]. The largest probability to encounter wake vortices shed by preceding aircraft prevails during final approach in ground proximity [2,3]. There clearance of the flight corridor by descent and advection is significantly restricted: stalling or rebounding vortices may not clear the flight corridor vertically and weak crosswinds may be compensated by vortex-induced lateral transport which may prevent the vortices to leave the corridor laterally. Moreover, the possibilities of the pilot to counteract the imposed rolling moment are restricted due to the low height of the aircraft above ground. Therefore, reliable wake–vortex prediction in ground proximity constitutes a vital requirement within a wake–vortex advisory system. The interaction of wake vortices with the ground was first considered in [4]. At first, the vortices induce a boundary layer (vorticity layer) at the solid surface which causes the wake vortices to diverge driven by mutual velocity induction. Another descriptive explanation of the phenomenon results from arguments of mass conservation: the diverging vortices circulate ambient air from their front sides (outboard) to their back sides (inboard) which in turn displaces the vortices laterally towards the outboard side. The effect is usually modeled by introducing image vortices that replace the former partner vortex aloft. Because of an adverse pressure gradient the boundary layer may separate subsequently which leads to the formation of secondary vortices. The interaction of primary and secondary vortices causes the former to detach from the hyperbolic trajectory of classical inviscid theory and the newly formed unequal vortex pairs rebound. This behavior was confirmed by numerical simulations [5–16], laboratory experiments [7,17], and field measurement data [18,19]. A survey on vortex interactions with walls is given in [20]. Two- dimensional simulations [6,8–10] indicate that crosswind shear may attenuate the formation of the secondary vortex on the luff (upwind) side whereas the secondary vortex on the lee (downwind) side is strengthened, a scenario which causes asymmetric rebound Presented as Paper 1077 at the 44th AIAA Aerospace Sciences Meeting and Exhibit, Atmospheric and Space Environments, Reno, NV, 9–12 January 2006; received 15 March 2006; revision received 28 June 2006; accepted for publication 29 June 2006. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code $10.00 in correspondence with the CCC. * Research Scientist, Institut für Physik der Atmosphäre; frank.holzaep- fel@dlr.de. † Student, Institut für Physik der Atmosphäre. AIAA JOURNAL Vol. 45, No. 1, January 2007 218