Radar has been proposed as a way to track wake vortices to reduce aircraft spacing and tests have revealed radar echoes from aircraft wakes in clear air. The results are always interpreted qualitatively using Tatarski's theory of weak scattering by isotropic atmospheric turbulence. The goal of the present work was to predict the value of the radar cross-section (RCS) using simpler models. This is accomplished in two steps. First, the refractive index is obtained. Since the structure of the aircraft wakes is different from atmospheric turbulence, three simple mechanisms specific to vortex wakes are considered: (1) Radial density gradient in a two-dimensional vortex, (2) three-dimensional fluctuations in the vortex cores, and (3) Adiabatic transport of the atmospheric fluid in a two-dimensional oval surrounding the pair of vortices. The index of refraction is obtained more precisely for the two-dimensional mechanisms than for the three-dimensional ones. In the second step, knowing the index of refraction, a scattering analysis is performed. Tatarski's weak scattering approximation is kept but the usual assumptions of a far-field and a uniform incident wave are dropped. Neither assumption is generally valid for a wake that is coherent across the radar beam. For analytical insight, a simpler approximation that invokes, in addition to weak scattering, the far-field and wide cylindrical beam assumptions, is also developed and compared with the more general analysis. The predicted RCS values for the oval surround the vortices (mechanism C) agree with the experiments of Bilson conducted over a wide range of frequencies. However, the predictions have a cut-off away from normal incidence which is not present in the measurements. Estimates suggest that this is due to turbulence in the baroclinic vorticity generated at the boundary of the oval. The reflectivity of a vortex itself (mechanism A) is comparable to that of the oval (mechanism C) but cuts-off at frequencies lower than those considered in all the experiments to date. The RCS of a vortex happens to peak at the frequency (about 49 MHz) where atmospheric radars (known as ST radars) operate and so the present prediction could be verified in the future. Finally , we suggest that hot engine exhaust could increase RCE by 40 db and reveal vortex circulation, provided its mixing with the surroundings is prevented in the laminarising flow of the vortices.

https://ntrs.nasa.gov/api/citations/20010003573/downloads/20010003573.pdf

Analysis of the Radar Reflectivity of Aircraft Vortex Wakes

Runway operation is the limiting factor for the overall throughput of airports. Today the International Civil Aviation Organization (ICAO) imposes wake vortex separation minima between following aircrafts that are based on simple pair-wise rules. However, the lifetime of wake vortices results from a much broader basis of factors, that ranges from a large set of aircraft parameters to meteorological conditions and traffic mix. In particular atmospheric conditions can significantly reduce wake hazard, for instance, in case of strong turbulence or crosswinds. While such situations could allow a reduction of the separation minima, safety reasons and the current technical challenges of detecting and managing such scenarios leads to the strict application of the ICAO standards. With the aid of accurate wind data and precise measurements of wake vortices, more efficient intervals could be set, particularly when weather conditions turn favourable. Depending on traffic intensity, these adjustments could enhance airport capacity, and generate major commercial benefits. This study deals with recent development in the radar technology to attain such goals. It presents (i) the trials of an electronic scanning radar to be used in a future wake turbulence advisory system and (ii) theoretical and numerical analysis of the radar response in clear air and in rainy weather. Part of this work has been achieved with the support of the European ATM research program SESAR.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-rsn.2015.0132

Radar wake-vortices cross-section/Doppler signature characterisation based on simulation and field tests trials

The present work is dedicated to the modeling and simulation of the radar signature of raindrops within wake vortices. This is achieved through the computation of the equation of raindrop motion within the wake vortex flow. Based on the inhomogeneous distribution of raindrops within wake vortices, the radar echo model is computed for raindrops in a given resolution cell. Simulated Doppler radar signatures of raindrops within wake vortices are shown to be a potential criterion for identifying wake vortex hazards in air traffic control. The dependence of the radar signature on various parameters, including the radial resolution and antenna elevation angle, is also analyzed.

Modeling the Radar Signature of Raindrops in Aircraft Wake Vortices

The study of scattering characteristics of a wake vortex is very important for hazard avoidance, especially near airports. Obtaining the dielectric constant distribution is one of the basic issues in the scattering study for radar detection. The present work proposes a modeling method for the dielectric constant distribution. In the method the dielectric constant variation (also the radar cross section (RCS)) due to the density variation and water vapor variation are studied. Research findings show that the density variation and water vapor variation serve as dominant factors to the RCS of a wake vortex in low frequency band and high frequency band, respectively.

Modeling the Dielectric Constant Distribution of Wake Vortices

La surveillance des turbulences de sillage par radar en temps de pluie presente un interet a la fois pratique et scientifique. Cette thematique a ete traitee a travers trois etapes successives.Tout d’abord, le mouvement et la distribution des gouttes d’eau dans les vortex ont ete modelises et simules. A partir de l’equation de la dynamique appliquee sur une goutte d’eau, une methode de calcul de la trajectoire des gouttes d’eau et de leur concentration dans les turbulences de sillage a ete proposee. Ensuite, deux simulateurs de reponse radar des gouttes d’eau dans et autour des vortex ont ete proposes. Ces deux simulateurs ont ete utilises pour reproduire des configurations experimentales, et une comparaison preliminaire avec les mesures a montre une concordance interessante entre mesures et simulations en bande X et W. Enfin, l’interpretation de la signature radar des gouttes de pluie dans les vortex a ete presentee. La dependance de la signature envers differents parametres, a savoir l’intensite de precipitation, la circulation des vortex et les parametres radar, a ete etudiee pour des turbulences de sillage generees par differents types d’avions. Une methode de detection des turbulences de sillage basee sur la largeur du spectre Doppler des gouttes de pluie et un algorithme permettant d’estimer les caracteristiques des turbulences de sillage ont ete proposees. La signature radar des turbulences de sillage par temps de pluie a ete modelisee et analysee dans cette these. Les resultats de simulations ont demontre les capacites du radar pour la detection de ces turbulences. Les methodes developpees dans cette these pourront etre utilisees pour le dimensionnement de systemes radar dedies a la surveillance des turbulences de sillage par temps de pluie.

Modélisation des signatures radar des tourbillons de sillage par temps de pluie

he Applied Physics Laboratory has built and fielded an experimental bistatic Xband continuous-wave radar system for studies in aircraft wake vortex detection. The radar, along with an acoustic pumping system, was installed at the BaltimoreWashington International Airport in the fall of 1996. Controlled experiments using a NASA C-130 aircraft were conducted on 23 September, 29 October, and 10 December. Results from two specific runs on 29 October are presented and discussed along with numerical simulations of those runs.

Aircraft Wake Detection Using Bistatic Radar: Analysis of Experimental Results

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Aircraft Wake Detection Using Bistatic Radar: Analysis of Experimental Results