Two-Dimensional Simulations of Wake Vortex Detection Using Radio Acoustic Sounding Systems

Abstract

Aparallelcodeisdevelopedtosimulatenumericallywakevortexdetectionusingaradioacousticsoundingsystem (RASS). The code is written in FORTRAN 90 with the message passing interface for parallel implementation. The numerical simulation solves simultaneously the linearized Euler equations for a nonuniform mean e ow and the Maxwellequationsforanonhomogeneousmedium.Theradartransmitterandreceiverantennasaremodeledusing an array of point sources and a beam-forming technique, respectively. Many features of the RASS are explored using thenumericalsimulation.First,a uniformmeane owisconsidered,and theRASSsimulation isperformedfor two different types of incident acoustic e eld: a short single-frequency acoustic pulse and a continuous broadband acoustic source. Both monostatic and bistatic cone gurations are examined, and their results are compared. Taylor and Oseen vortex velocity proe les are used as samplemodels, and their mean e owe eldsare reconstructed from the backscattered electromagnetic signal using the Abel transform. The effect of radar beam width is also considered, as are the issues of nonaxisymmetric and interacting vortices. I. Introduction T HEcapacity of airports is constrainedseverelyby the airtrafe c control system’ s consideration of aircraft wake vortices. The present Instrument Flight Rules (IFR) restrictions are based on aircraft weight. The “ 3‐ 4‐ 5‐ 6 rule” sets the separation distances of aircraft by categories from small, less than 41,000 lb (18,600 kg), to heavy, greater than 255,000 lb (116,000 kg). These separations are viewed as very conservative. However, because there remains signie cant uncertainty about wake vortex behavior under different atmospheric conditions, there are considerable technological barriers to improvements in terminal area productivity. In an attempt to enhance airport capacity, an aircraft vortex spacing system (AVOSS) has been under development at NASA Langley Research Center. The AVOSS will provide the means to allow air trafe c control to reduce spacing safely in instrument operations when the appropriate weather conditions exist. A key element in AVOSS is the development of a real-time reliable wake vortex detection system (WVDS). A radio acoustic sounding system (RASS) is a promising candidate for a WVDS. The basic concept of RASS is based on the tracking of sound waves with radar. When acoustic waves are transmitted, they produce pressure perturbations, which lead to e uctuations in the atmospheric permittivity. An incident electromagnetic e eldisthenscatteredduetothepermittivityvariationsandgenerates an echo that can be detected by a receiver antenna. The spectrum of this echo shows a Doppler shift proportional to the local speed of sound. However, the backscattered signals are so weak that no measurable signal would be received unless the Bragg condition is satise ed.The Bragg condition is a relationshipbetween the incident electromagnetic and acoustic wavelengths that ensures a constructive interference between the two waves. The Bragg condition may be written as ¸e D 2¸a sin®