Frank Holzäpfel

Commercial aircraft wake vortices

Abstract This paper discusses the problem of wake vortices shed by commercial aircraft. It presents a consolidated European view on the current status of knowledge of the nature and characteristics of aircraft wakes and of technical and operational procedures of minimizing and predicting the vortex strength and avoiding wake encounters. Methodological aspects of data evaluation and interpretation, like the description of wake ages, the characterization of wake vortices, and the proper evaluation of wake data from measurement and simulation, are addressed in the first part. In the second part an inventory of our knowledge is given on vortex characterization and control, prediction and monitoring of vortex decay, vortex detection and warning, vortex encounter models, and wake-vortex safety assessment. Each section is concluded by a list of questions and required actions which may help to guide further research activities. The primary objective of the joint international efforts in wake-vortex research is to avoid potentially hazardous wake encounters for aircraft. Shortened aircraft separations under appropriate meteorological conditions, whilst keeping or even increasing the safety level, is the ultimate goal. Reduced time delays on the tactical side and increased airport capacities on the strategic side will be the benefits of these ambitious ventures for the air transportation industry and services.

Probabilistic Two-Phase Wake Vortex Decay and Transport Model

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

The turbulent decay of trailing vortex pairs in stably stratified environments

The decay of trailing vortex pairs in thermally stably stratified environments is investigated by means of large eddy simulations. Results of in-situ measurements in the wakes of different aircraft are used to find appropriate intitializations for the simulation of wake turbulence in the quiescent atmosphere. Furthermore, cases with weak atmospheric turbulence are investigated. It is shown that the early development of the vortices is not affected by turbulence and develops almost identically as in 2D simulations of wake vortices in stably stratified environments. In a quiescent atmosphere the subsequent vortex decay is controlled by the interaction of short-wave disturbances, owing to the aircraft induced turbulence, and baroclinic vorticity, owing to stable stratification. As a consequence, vertical vorticity streaks between the vortices are induced which are substantially intensified by vortex stretching and finally lead to rapid turbulent wake-vortex decay. When in addition atmospheric turbulence is also present, the long-wave instability is dominantly promoted. For very strong stratification ( Fr < 1) it is observed that wake vortices may rebound but lose most of their strength before reaching the flight level. Finally, the simulation results are compared to the predictive capabilities of Greene’s approximate model.  2001 Editions scientifiques et medicales Elsevier SAS

Analysis of Wake Vortex Decay Mechanisms in the Atmosphere

Abstract Results of high-resolution numerical simulations of aircraft wake vortex evolution and decay in different regimes and atmospheric conditions are presented. The different cases comprise (i) the near field interaction of a trailing vortex with an exhaust jet, (ii) the evolution of single vortices and counter-rotating vortex pairs in homogeneous isotropic turbulence, as well as (iii) the decay of wake vortices in a turbulent stably stratified atmosphere, and (iv) in a weakly turbulent sheared environment. The different cases are used to analyse common aspects of vortex dynamics and decay mechanisms. In all scenarios the formation of coherent secondary vorticity structures that enclose the primary vortices is observed. These secondary vorticity structures deform and weaken the primary vortices and in some cases lead to rapid vortex decay. It is shown that the mean swirling flow effectively rearranges and intensifies any secondary vorticity by tilting and stretching. The secondary vorticity may either originate from the turbine jet, ambient turbulence or may be produced baroclinically. Based on the observed phenomena, eleven postulates are established that pinpoint fundamental aspects of the observed decay mechanisms.

Probabilistic Two-Phase Aircraft Wake-Vortex Model: Further Development and Assessment

Further developments, applications, and assessments of the probabilistic two-phase aircraft wake-vortex model P2P are described. The wake-vortex model is applied to data of two field measurement campaigns accomplished at Tarbes airport, France. Measurements corroborate unambiguously the two-phase circulation decay anticipated by theory and predicted by P2P. Vortex age and descent speed are adjusted to match effects of axial wind and glide slope angle. Envelopes of vortex trajectories are expanded to consider tilting, stalling and rebounding wake vortices caused by axial- and crosswind shear. For probabilistic model output a choice between arbitrary degrees of probability is established and a stochastic prediction mode is introduced. In a deterministic scoring procedure, model perfomance is compared to the skill of another model. Probabilistic model performance is evaluated by the compilation of probability density distributions which relate wake vortex measurement data to the predicted envelopes.

Probabilistic Two-Phase Aircraft Wake Vortex Model: Application and Assessment

Predictions of the parametric probabilistic two-phase aircraft wake-vortex transport and decay model P2P are compared with field observations. The two-phase decay model predicts probabilistic wake-vortex behavior as a function of aircraft and environmental parameters in real time. Observation data from field deployments accomplished at the International Airports Memphis and Dallas Fort Worth and from the WakeOP campaign performed at the airfield in Oberpfaffenhofen, Germany, are employed. In a scoring procedure, the predictive capabilities of a deterministic version of P2P are compared to Sarpkayas model

Wing-tip vortices, turbulence, and the distribution of emissions

The decay of wing-tip vortices under the Influence of turbulence in a stably stratified atmosphere is discussed by means of large-eddy simulations. The vortices originate from a B-747 aircraft in cruise. Atmospheric turbulence and turbulence originating from the boundary layer around the aircraft are distinguished. The former is weak and anisotropic with eddy sizes in the order of the wing span, whereas the latter is wrapped around the vortices with the maximum intensity at the core diameter. During their descent, the parallel vortex tubes approach each other because stratification and turbulence detrain mass into the ambient air. The atmospheric eddies deform the trailing vortices such that their spacing varies. This, in turn, yields different mutually induced velocities that amplify the deformation quickly according to Crows instability theorem. The bent vortex tubes link after about 1.5 min and form rings. The continuous trail of turbine exhaust is reorganized in a row of single puffs

Wake Vortices in Convective Boundary Layer and Their Influence on Following Aircraft

The decay of three wake vortex pairs of a B-747 aircraft in an evolving and convectively driven atmospheric boundary layer is investigated by means of large-eddy simulations (LES). Convective boundary layers are considered hazardousbecausetheupdraft velocitiesofa thermalmay compensatetheinduceddescent speed ofthevortex pair such that the vortices stall in the e ight path. The LES results illustrate that 1 )the primary rectilinear vortices are rapidly deformed on the scale of alternating updraft and downdraft regions; 2 ) parts of the vortices stay on e ight level but are quickly eroded by the turbulence of the updraft; 3 )the longest living sections of the vortices are foundinregionsofrelativelycalmdownwarde ow,which augmentstheirdescent.Striptheory calculationsareused to illustrate the temporal and spatial development of lift and rolling moments experienced by a following medium weight class B-737 aircraft. Characteristics of the respective distributions are analyzed. Initially, the maximum rolling moments slightly exceed theavailableroll controloftheB-737. After60 sthe probability ofrolling moments exceeding 50% of the roll control has decreased to 0.009% in a safety corridor around the glide path. Nomenclature b = aircraft span b0 = initial vortex spacing c = section chord cl = section lift coefe cient dP = probability difference g = gravitational acceleration k = wave number

Strategies for Circulation Evaluation of Aircraft Wake Vortices Measured by Lidar

An assessment of different methods for circulation evaluation from lidar measurement data of aircraft wake vortices is performed. The surface integral of vorticity serves as baseline case that is compared to a method that evaluates the lidar line-of-sight velocity midway between the vortices and to another method that calculates radii averages of circulations derived from tangential velocities. Systematic deviations from nominal circulation are discussed based on analytical vortices. High-resolution numerical simulation data are applied to perform virtual lidar measurements that reproduce, explain, and quantify (i) the frequently observed initial overestimation of circulation and (ii) the scatter of circulation data caused by the genuine variability of wake vortices in the atmospheric boundary layer. The theoretically derived characteristics of the different evaluation methods are verified against lidar data recorded by several lidar teams during the Wake Vortex Forecasting and Measuring Campaign at Oberpfaffenhofen (WakeOP), performed in spring 2001 at Fairchild Dornier Airport in Oberpfaffenhofen, Germany.

Vortex bursting and tracer transport of a counter-rotating vortex pair

Large-eddy simulations of a coherent counter-rotating vortex pair in different environments are performed. The environmental background is characterized by varying turbulence intensities and stable temperature stratifications. Turbulent exchange processes between the vortices, the vortex oval, and the environment, as well as the material redistribution processes along the vortex tubes are investigated employing passive tracers that are superimposed to the initial vortex flow field. It is revealed that the vortex bursting phenomenon, known from photos of aircraft contrails or smoke visualization, is caused by collisions of secondary vortical structures traveling along the vortex tube which expel material from the vortex but do not result in a sudden decay of circulation or an abrupt change of vortex core structure. In neutrally stratified and weakly turbulent conditions, vortex reconnection triggers traveling helical vorticity structures which is followed by their collision. A long-lived vortex ring links ...