NASA Technical Reports Server (NTRS) 20040110857: Numerical Simulation of Wake Vortices Measured During the Idaho Falls and Memphis Field Programs PDF
Preview NASA Technical Reports Server (NTRS) 20040110857: Numerical Simulation of Wake Vortices Measured During the Idaho Falls and Memphis Field Programs
Numerical Simulation of Wake Vortices Measured During the Idaho Falls and Memphis Field Programs Fred H. Proctor NASA Langley Research Center Flight Dynamics & Control Division Hampton, VA 23681-0001 14th AIAA Applied Aerodynamic Conference 17-20 June 1996, New Orleans, Louisiana AIAA Paper No. 96-2496 NUMERICAL SIMULATION OF WAKE VORTICES MEASURED DURING THE IDAHO FALLS AND MEMPHIS FIELD PROGRAMS Fred H. Proctor NASA Langley Research Center Flight Dynamics & Control Division Hampton, VA 23681-0001 Abstract turbulence, for example, may lessen the threat of a dangerous wake vortex encounter, and thus allow a A numerical large-eddy simulation model is tightening up of wake vortex separation standards now under modification and testing for application to aircraft in effect during instrument meteorological conditions. wake vortices. The model, having a meteorological framework, permits the interaction of wake vortices with NASA-Langley theoretical modelling efforts are environments characterized by crosswind shear, stratifi- expected to play a major role in the development of cation, and humidity. As part of the validation process, these algorithms. A numerical large-eddy simulation model results are compared with measured field data model called the Terminal Area Simulation System2 from the 1990 Idaho Falls and the 1994-1995 Memphis (TASS) has been modified for application to aircraft field experiments. Cases are selected that represent wake vortex simulations. The TASS model, which is different aircraft and a cross section of meteorological described in section 2, is believed to have an advantage environments. Also included is one case with wake over other wake vortex models3,4,5,6,7,8 in that it has a vortex generation in ground effect. The model simula- meteorological reference frame, compressible non- tions are initialized with the appropriate meteorological Boussinesq equation set, subgrid turbulence closure, a conditions and a post roll-up vortex system. No am- formulation for ground-friction, realistic boundary bient turbulence is assumed in our initial set of experi- conditions, an option for either two or three spatial ments, although turbulence can be self generated by the dimensions, and accurate -- yet computationally efficient interaction of the model wakes with the ground and -- numerical approximations. In spite of the model's environment. sophistication, it has relatively fast execution times, which is an important feature when taking on the I. Introduction ambitious task of simulating three-dimensional, time- dependent aircraft wakes. The TASS model is capable In response to a continuing trend for increased of simulating post roll-up wake vortices in both two and air travel that has led to more frequent delays and three dimensions, for a wide range of atmospheric increased costs to air carriers and the traveling public, conditions that include: vertical wind shear, NASA through its Terminal Area Productivity (TAP) stratification, atmospheric boundary layer turbulence, program is developing systems that will increase fog, and precipitation. Initial emphasis is being placed efficiency, yet ensure safety to the traveling public. A on validation. Once this has been accomplished with major element to this program is the development of an sufficient confidence, then TASS model output will be automated system called the Aircraft Vortex Spacing used to develop parametric relationships for vortex System (AVOSS) -- which will determine safe operating transport and decay as related to different aircraft types spacings between arriving/departing aircraft as based on (e.g., B-767, DC-10, etc.) and meteorological conditions the observed/predicted weather state.1 At the core of (windshear, stratification, ambient turbulence, humidity AVOSS will be a predictor algorithm that relates the and precipitation). The model can also provide high transport and decay of aircraft wake vortices to the spatial resolution fields of wind, pressure, temperature, present and future weather state. The presences of and humidity, for analyzing and understand the structure strong crosswinds and vigorous environmental of wake vortices. The generated high-resolution fields Copyright © 1996 by the American Institute of Aeronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herin for government purposes. All other rights are reserved by the copyright owner. will be valuable in the characterization and quanti- Table 1. Salient Characteristics of TASS 6.x fication of wakes generated in various meteorological AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA scenarios, as well as for providing realistic data sets for AAAAAAAAPAAAAriAAmAAAAitAAivAAAAeAA AAeAAqAAuAAAAaAAtAAioAAAAnAA AA/ AAnAAAAoAAnAA-AABAAAAoAAuAAsAAsAAAAinAAAAeAAsAAqAA AAeAAAAqAAuAAaAAtAAiAAoAAnAA AAsAAeAAAAtAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA wake vortex sensor development. AAAAAAAATAAiAAmAAAAeAA-AAdAAeAAAApAAeAAnAAdAAAAeAAnAAtAA,AA nAAAAoAAnAAhAAAAyAAdAArAAoAAsAAtAAaAAtAAiAAcAA, AAcAAoAAAAmAAAApAArAAeAAsAAsAAiAAbAAlAAeAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA The purpose of this paper is to give an over- AAAAAAAAMAAAAeAAtAAeAAoAArAAoAAAAloAAgAAAAicAAaAAAAl AAAAfrAAaAAmAAAAeAAAAwAAoAAAArkAA AAAAwAAAAitAAhAA AAAAoAApAAtAAioAAAAnAA AAfAAoAArAA AAAAeAAitAAhAAeAAAArAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA view of the TASS model and to present results of its AAAAAAAAtAAhAArAAeAAeAA-AAdAAiAAmAAAAeAAnAAsAAAAioAAnAAAAaAAlAA oAAAAr AAtAAwAAAAoAA-AAdAAimAAAAeAAAAnAAsAAiAAoAAnAAaAAAAl AAsAAiAAmAAuAAAAlaAAAAtiAAoAAnAAsAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA application to wake vortex research. Two-dimensional AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA simulations of cases from the 1990 FAA Idaho Falls AAAAAAAALAAiAAqAAuAAiAAdAA AAaAAnAAAAdAA AAicAAeAAAA pAAAAhAAaAAsAAAAeAA AAmAAiAAcAArAAoAApAAAAhAAyAAsAAiAAcAAsAA AA-AA- AAcAAaAAAAnAA AAsAAimAAAAuAAAAlaAAtAAeAAAAAAAAAA and from the Memphis 1994 and 1995 NASA/MIT- AAAAAAAAAAAAgAAArAAAoAAAwAAAAAAtAAAhAAA AAApAAAAAAroAAAAAAcAAAeAAAsAAAsAAAAAAeAAAsAAA AAAAAAfoAAAAAAr AAAAAAcAAAloAAAAAAuAAAdAAA AAAAAAdAAArAAAoAAApAAAAAAleAAAtAAAsAAA,AAA AAAcAAAlAAAoAAAuAAAAAAdAAA AAAiAAAcAAAeAAAAAAAAAAAAAAA AAAAAAAAcAArAAyAAsAAtAAaAAlAAsAA,AA AAraAAAAinAA,AA AAsAAnAAoAAAAwAA AAaAAAAnAAdAA AAhAAAAaAAiAAl.AA AAAAAAAcAAcAAAAoAAmAAAApAAlAAisAAhAAAAeAAdAA AAwAAAAitAAhAAAAAAAAAA Lincoln-Laboratory wake-vortex field deployments are AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAlaAAAArgAAAAeAA AAsAAeAAtAA oAAAAf AAmAAAAicAAAAroAAAApAAhAAyAAsAAAAicAAaAAAAl-AApAAaAArAAaAAAAmAAeAAAAteAAAAriAAzAAaAAtAAiAAoAAnAA AAmAAAAoAAdAAeAAAAlsAAAAAAAAAA presented. Results from the computational simulations, AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA including comparisons with measurements, are presented AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAIAnAvAeArAsAeAA-eAAxApAoAAnAeAnAtAiAaAl AsAiAzAeA AdAiAsAtrAiAbAuAtAioAAnAsA AfoAAr ApArAeAcAAipAiAtAaAt-AAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA for the Idaho Falls cases in section 4 and for the AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAinAAgA AhAyAdAAroAAmAAeAtAeAoArAsAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Memphis cases in section 5. Details of the TASS AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA model are described in the next section and the initial- AAAAAAAALAAaAAAArgAAAAeAA AAEAAdAAAAdAAyAA AASAAAAimAAAAuAAAAlaAAtAAiAAoAAnAA AAmAAAAoAAdAAAAeAAl AAwAAAAiAAthAAAA 1AAAAsAAtAA-oAAAArdAAAAeAArAA AAsAAuAAbAAAA-AAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ization procedure is reported in section 3. AAAAAAAAgAArAAiAAdAA sAAcAAAAaAAlAAeAA tAAuAArAAbAAuAAAAleAAnAAAAcAAeAA AAcAAloAAAAsAAuAArAAeAA AA-AA- AAsAAcAAaAAlAAeAAsAA AAoAAfAA tAAuAArAAbAAuAAAAleAAnAAAAcAAeAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAlaAAAArgAAAAeAArAA AAAAthAAAAaAAnAA AAAAgAAAAriAAdAA AAAAvAAoAAlAAuAAmAAAAeAAAA AAaAAAAreAAAA AAAAreAAAAsAAoAAlAAvAAeAAdAAAA AAiAAnAA AAAAtAAhAAeAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA II. Model Description AAAAAAAAsAAiAAmAAAAuAAlaAAAAtiAAoAAnAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAGAArAoAuAnAdAA sAAtrAeAsAsAA bAAaAsAeAdAA oAAnA AMAAoAnAiAnA-AOAAbAuAkAhAAoAvA ASAiAmAAilAaArAitAyAAAAA The TASS model is a multi-dimensional, large- AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAtAhAeAoAAryAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA eddy code that has been used to study a variety of AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA meteorological phenomenon including convective local AAAAAAAAAAAACAAAAAAhAAAoAAAiAAAcAAAeAAA AAAoAAAfAAA AAAlaAAAAAAteAAAAAAraAAAAAAl AAAbAAAoAAAAAAuAAAnAAAdAAAAAAaAAArAAAieAAAsAAAAAA: AAAmAAAAAAaAAAyAAAAAA bAAAAAAeAAA AAAeAAAiAAAthAAAAAAeAAArAAA oAAAAAApAAAeAAAnAAAAAA,AAAAAAAAAAAA storms,9 microburst/windshear,10,11,12,13 hailstorms,14 AAAAAAAAAAAAmAAAAAAirAAArAAAoAAArAAA,AAA oAAAAAAr AAApAAAAAAeAAArAAAioAAAAAAdAAAicAAAAAA -AAA-AAA AAAoAAApAAAeAAAAAAnAAA AAAcAAAoAAAnAAAAAAdAAAitAAAiAAAoAAAnAAA AAAuAAAtAAAilAAAizAAAAAAeAAAsAAA AAAmAAAAAAaAAAsAAAsAAAAAA-AAAAAAAAAAAA tornadic thunderstorms,15 nuclear cloud rise,16 and AAAAAAAAAAAAcAAAoAAAnAAAAAAsAAAeAAArAAAvAAAaAAAAAAtiAAAvAAAeAAA,AAA AAAAAAnAAAoAAAAAAnAAArAAAeAAAfAAAleAAAcAAAAAAtiAAAvAAAeAAA AAAAAArAAAaAAAdAAAAAAiaAAAAAAtiAAAoAAAnAAA AAAAAAAAAbAAAoAAAuAAAnAAAAAAdAAAaAAArAAAyAAAAAAAAAAAAAAA atmospheric boundary layer turbulence.17,18 The TASS AAAAAAAAAAAAsAAAcAAAhAAAAAAeAAAmAAAAAAeAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA model has been validated with observed data for a AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA range of micro- and cloud-scale phenomena, and was AAAAOAApAtAioAAnA AAfoAArA AAnAoAnAsAAtaAAtiAoAnAaAAryAA AAdAoAmAAaAiAnA AA-A-A AAmAAoAvAaAAbAleAA,AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA highly successful in the completed NASA-FAA wind- AAAAsAtAoArAmAA/vAAoArAteAAxA AcAeAnAtAeArAiAnAgA AmAAeAsAhAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA shear program. Recent modifications to the initial AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA conditions allow for its application to aircraft wake AAAAAAAAEAAAAxAApAAlAAicAAiAAt AAnAAuAAmAAAAeAAAAriAAcAAaAAlAA sAAcAAhAAAAeAAmAAAAeAAsAAAA, AAqAAuAAaAAdAAAArAAaAAtiAAcAA cAAAAoAAnAAsAAeAAAArAAvAAaAAtAAivAAeAAAA,AAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA vortex phenomenon. Thus the model is not merely a AAAAAAAAtAAimAAAAeAA-AAsAApAAAAliAAt AAAAcAAAAoAAmAAAApAArAAeAAsAAsAAAAibAAlAAeAA-AA-AA AAAAaAAcAAcAAuAAAArAAaAAteAAAA AAAAaAAnAAAAdAA AAAAhAAiAAgAAhAAAAlyAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA "wake vortex model," but can be generically applied to AAAAAAAAeAAfAAfiAAcAAiAAeAAnAAtAA, AAaAAAAlmAAAAoAAsAAAAt AAnAAoAAAA nAAAAuAAmAAAAeAArAAiAAcAAaAAlAA dAAAAifAAfuAAAAsAAioAAAAnAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA a diversity of phenomena. The model includes parame- AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAraAAAAkAAaAAwAAAAaAA AAAACAAAA-gAAAAriAAdAA AAAAsAAtAAaAAgAAgAAAAeAArAAeAAdAA AAAAmAAAAeAAsAAAAhAA, AAAAaAAAAnAAdAA AAAAvAAeAArAAtAAicAAAAaAAlAAAAAAAA terizations for ground stresses that are a function of AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAcAAoAAoAAAArAAdAAinAAAAaAAtAAeAA AAsAAtAAreAAAAtcAAhAAAAinAAAAgAA AAaAAllAAoAAwAAAAeAAdAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA surface roughness, allowing for "in-ground effect" wake AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA simulations with realistic ground interactions. AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAFAiAltAeArA AaAnAdAA sAApAoAnAgAAeA AaApApAAliAeAdA AtAoA AtoAApA AfoAAuArA rAoAwAAsA AsAoA AaAsAA tAoAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAdAiAmAAinAAisAhAA gAAraAAvAitAyA AwAAaAvAeAA rAeAfAlAeAcAtAioAnAA AaAt AtAoApAA bAAoAuAnAAdAaArAyAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA The TASS model consists of 12 prognostic AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA equations: three equations for momentum, one equation AAAAAAAAAAAAAmAAbAAAAieAAAAnAAtAA AAaAAAAtmAAAAoAAsAAAApAAhAAeAAAAriAAcAA AAAAcAAoAAnAAdAAAAitAAioAAAAnAAsAA AAAAinAAAAitAAiaAAAAliAAzAAeAAdAAAA AAwAAAAitAAhAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA each for pressure deviation and potential temperature, AAAAAAAAvAAeAArAAtAAicAAAAaAAl AApAArAAoAAfAAilAAeAA AAoAAfAA AApAArAAeAAsAAAAsAAuAArAAeAA AAoAArAA aAAAAltAAitAAuAAdAAAAeAA,AA tAAeAAmAAAApAAeAAAAraAAAAtuAAAAreAAAA,AAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA six coupled equations for continuity of water substance AAAAAAAAdAAeAAAAwAA AApAAoAAAAinAAAAt,AA AAaAAnAAdAAAA wAAAAiAAnAAdAA AAvAAeAAlAAoAAcAAiAAtAAyAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA (water vapor, cloud droplet water, cloud ice crystals, AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAMAAAAoAAdAAAAeAAl AAAAaAApAAAApAAlAAicAAaAAAAbAAleAAAA AAtAAoAA AAAAmAAAAeAAAAsAAoAA-AAgAA AAAAaAAnAAdAA AAAAmAAAAiAAcAArAAoAA AAAAsAAcAAaAAAAleAAAAAAAAAA rain, snow and hail) and a prognostic equation for a AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAaAtAmAAoAsApAAhAeArAiAcA pAhAAeAnAoAAmAAeAnAoAAnA. AInAAitAiaAAliAzAaAtAioAAnA mAAoAAdAuAlAeAsA AfoAArAAAA massless tracer. The non-Boussinesq formulation used AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAsAAiAAmAAAAuAAlaAAAAtiAAoAAnAA AAAAAAoAAf AAAAAAcAAoAAnAAvAAAAeAAcAAtAAivAAeAAAA AAAAsAAtAAoAArAAmAAAAsAA, AAAAAAmAAAAicAArAAoAAbAAAAuAArAAsAAtAAsAA,AAAAAAAA in TASS was initially developed to study tornadoes with AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAaAAtAAmAAAAoAAsAApAAAAhAAeAArAAiAAcAA AAbAAoAAAAuAAnAAdAAAAaAArAAyAA AAlAAaAAyAAeAArAAsAA,AA AAaAAAAnAAdAA AAaAAAAirAAcAArAAaAAfAAtAA AAwAAAAaAAkAAeAAAAAAAAAA application to similar intense vortices.19 This AAAAAAAAAAAAvAAAoAAArAAAtAAAicAAAAAAeAAAsAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA formulation was subsequently extended to a com- AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA pressible time-split formulation, and parameterizations AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA for numerous microphysical interactions were included model are listed in table 1. as an option.2 Salient characteristics of the TASS 2 American Institute of Aeronautics and Astronautics The TASS equation set in standard tensor Conservation of Scalar Variables (e.g., water vapor, notation is as follows: cloud droplet water, etc.) Momentum: ¶ Q 1 ¶ Q r o u j Q r¶ o u j 1 ¶ S j ( Q ) s ¶ t r ¶ x r ¶ x r ¶ x Q ¶ ¶ u t i rH ¶ ¶ xp ¶ ¶u xi u j ui ¶¶ ux j g(H 1)d i3 where sQ reporesentjs contriobutionj fromo sourcje terms. o i j j For precipitating variables (such as rain and snow), an t¶ 2W (u u )e 1 i j additional vertical flux term is added to the above j k ok ijk r ¶ x equation to account for fall out. o j Buoyancy Term: The dependent variables in TASS are treated as q pC averages over the grid volumes -- giving rise to subgrid H [ q P C v ] [1 0.61 (Qv Qvo) QT] Reynold's stress and subgrid eddy transport terms. o o p From first-order closure theory, the subgrid scalar covariances and subgrid stress are respectively: Pressure Deviation: ¶ Q S (Q) r K ¶ p C p P ¶ u j r gu d C p P d q j o H ¶ xj ¶ t C ¶ x o j j3 C q dt V j v t r K [ ¶ u i ¶ u j 2 ¶ u k d ] r K D ij o M ¶ x ¶ x 3 ¶ x ij o M ij Thermodynamic Equation (Potential Temperature): j i k q¶ 1 q¶r o u j q ¶r o u j 1 ¶ S j ( q ) Ath em soudbigfireidd eSdmdayg voirsincosksiyt yf:irst-order closure is used for ¶ t r ¶ x r ¶ x r ¶ x o j o j o j T Cq p [Lvsv Lfsf Lsss] KM ls2 ¶ ¶ ux i ( ¶¶ ux i ¶¶ ux j ) 23 ( ¶¶ ux k ) 2 × 1 R f j j i k with the Potential Temperature being defined as: The subgrid eddy viscosity is modified by stratification R d through the Flux Richardson Number, Rf , which is q T ( P o o )Cp approximated from the Richardson number, Ri, as: P R = Min[ 0.9998, Ri K /K ], In the above equations, u is the tensor component of f H M i velocity, t is time, p is deviation from atmospheric where the subgrid eddy viscosity for heat is specified as pressure P, T is atmospheric temperature, r is the air K = 3 K . The Richardson number for moist, but density, W is the earth's angular velocity, C and C are H M p v unsaturated air is20 the specific heats of air at constant pressure and volume, cgo inss tthaen te faorrth d'sr yg arairv, iPtati oisn aal caocncsetlaenrta teiqouni,v aRlde nist ttoh e1 0g0a0s 1 ¶ P ¶ q ( 1 0 . 6 1 Q v Q T ) oo r q ¶ x ¶ x millibars (105 pascals) of pressure, Q is the mixing Ri o k k v ratio for water vapor, and Q is the sum of the mixing D2 T ij ratios for liquid and ice water substance, L is the latent v For saturated air (i.e. 100% relative humidity) the heat for vaporization for water, L is the latent heat for f Richardson number is modified from above to account fusion for water, L is the latent heat for sublimation s for the moist adiabatic ascent and descent of saturated for water, and s , s , and s are the respective water v f s air parcels. Therefore, (1/q )¶q /¶ z is replaced with: substance source terms. Environmental state variables, e.g., u , Q , r , and q , are defined from the ok vo o o initial input sounding and are functions of height only. 3 American Institute of Aeronautics and Astronautics generating aircraft. In the event of strong crosswinds, e L e wide domains are not needed since the numerical grid P v v translates with the horizontal advection of the wake 1 ¶q g 1 R d T vortices. The top of the domain is chosen at least 50 m q ¶ z CpT P e L v 2 e v afoblolovwe itnhge caalsteitsu, dthe eo hf otrhizeo ngteanle draotminagi na sirizcera ifst . beItnw etehne C R T2 p v 150 m and 300 m wide and the vertical depth is be- where R is the gas constant for water vapor, e = tween 100 m and 250 m. The simulations use the open v radiation boundary condition option at the two lateral R /R , z is the vertical coordinate, and e is the vapor d v v boundaries, allowing minimal interference and distortion pressure for liquid water. The subgrid length scale, l , s to the interior flow. is determined from the grid volume and is matched to the appropriate length scale close to the ground where Ambient Conditions the flow is under-resolved. That is: Each case is initialized with its respective vertical distribution of observed temperature, dewpoint, aD z ‡ aD /k and wind velocity, that represents the air mass surround- aD [1 (aD /kz)m 1] l aD /k > z > D z/2 ing the wake. Horizontal variations in the ambient s 1 (aD /kz)m conditions are not considered. kz z £ D z/2 where k is von Karman's constant, and where m and a Vortex Initialization As for the initial wake field, the two-dimen- are invariant constants with values defined as m = 2.5 and a = 0.155. The filter width is sional simulations are initialized with a simple vortex system that is representative of the post roll-up, wake D [2D x 2D y 2D z]1/3 velocity field. The vortex system is initialized with the superposition of two counter-rotating vortices, with the where D x, D y, and D z are the numerical grid sizes in the velocity field for each vortex according to the Burnham- respective x, y, z direction. Hallock model21 as: The ground boundary is impermeable (except G to precipitation) with nonslip velocity specifications. V(r) ¥ r Surface stresses are computed locally from the near- 2p rc2 r2 ground wind velocity, Richardson number, and surface where V is the vortex tangential velocity, r the radius, roughness height. r is the core radius (i.e. radius of peak tangential c An abbreviated discussion of the numerical velocity), and G ¥ the circulation at r >> rc. Appropri- ate vortex image conditions are applied to the initial approximations for the TASS equation set can be found wake field to ensure consistency and mass continuity at in the Appendix. the model boundaries. III. Initial Conditions The parameters that govern the vortex initial- ization are: vortex separation, core size, height, and Grid/Domain Configuration circulation. The height of the vortex system, Z, is For the simulations presented in this paper we i determined from the observed height of the generating have chosen the 2-D option for all simulations with D x aircraft. The vortex core radius is assumed to be 5% of = D y = D z , and have rotated the coordinate system the generating aircraft's span. The remaining parameters such that y is along the aircraft flight path and x in the are aircraft dependent and can be obtained from aerody- cross track direction; z represents distance above the namic theory with the assumption of an elliptically- ground. The simulations are time integrated within the loaded wing22 as: two-dimensional x-z plane. In the cases presented here, a constant grid size of 3/4 to 1 meter is used. S p B G 4 M g 4 ¥ pr V B a The computational domain size for each case simulation is governed by the size and height of the 4 American Institute of Aeronautics and Astronautics where S is the vortex separation, B is the span of the Atmospheric data were measured by the tower and a generating aircraft, V is the true air speed, and M is the tethersonde. The tests were conducted in September a mass of the generating aircraft. during mornings and extending into early afternoons. The prevalent atmospheric conditions were dry and This initialization procedure does not account stable with local drainage flows -- transitioning as the for the aircraft configuration (i.e. flap settings, landing morning progressed -- to an unstable boundary layer that gear, inclined flight path); however, results from this grew in depth due to solar heating. procedure were found to give good comparisons with observations regardless of flight configuration. From this data set, seven cases were chosen that represent a range of atmospheric conditions and Turbulence Initialization aircraft types (table 2). Characterization of the meteorol- All of the following cases assume that there is ogical conditions are represented by several parameters no preexisting ambient turbulence. However, turbulence (also listed in table 2), which are: the vertical change in (and the effects of turbulence) can develop in the potential temperature Dq /D z (negative for unstable simulations from the interaction of the wakes with either stratification, positive for stable), mean crosswind shear the ground or ambient environment. This assumption of D U/D z , crosswind at flight level U(Z) , and a Bulk I no initial turbulence is acceptable for stably-stratified Richardson number based on the crosswind flow, i.e., environments, since the affect of vortex generated turbulence likely overwhelms the affect due to any Ri g D q / D z preexisting turbulence. Currently, an initialization for b q (D U/D z)2 ambient turbulence is being developed, and future where the mean gradients in the listed parameters are studies will evaluate its effect in both two- and three- taken between 5 m AGL and 15 m above the flight dimensional wake simulations. path. Execution Time Model validation experiments were conducted The TASS code can be run on any modern for each of the seven cases, with the input for ambient computer or workstation that is equipped with a fortran conditions constructed from the tower and tethersonde compiler. However, the domain size and grid resolution data. The tower provided excellent ambient wind and will be limited by the host computer's memory and temperature information up to 61 m. At higher eleva- speed of execution. A typical two-dimensional wake tion the tethersonde data was used, which unfortunately, vortex simulation with a 1-m grid resolution takes about was of lesser quality, being subject to errors from very- 20 min of CPU time on a Cray C-90 supercomputer. short averaging times and bobbing of the balloon. For a fixed domain, the execution time is inversely Values for the initial vortex parameters (also included in proportional to the cube of the grid size. So a doubling table 2) were determined from aircraft dependent (halving) of the resolution can increase (decrease) the specifications and the reported weight, height, and speed execution time by a factor of eight. of the generating aircraft. Comparison of the simula- tions with the measured data was generally very good IV. Results -- Idaho Falls with computed vortex trajectories having the best agreement. Good agreement was obtained independent The first set of TASS validation experiments of flight configuration and aircraft type. Comparison of are from the 1990 Idaho Falls, Idaho (IDF) field model circulation values tended to upper-bound the experiment. The principal aim of this FAA sponsored observations, with the measurements indicating greater field study was to evaluate Boeing 757 and 767 aircraft decay rates after one or two minutes. This was better wakes in a week-long series of tower fly-bys. An than expected since the two-dimensional simulations do extensive data set was generated by a DOT/NOAA team not allow vortex stretching and do not permit develop- containing wake vortex measurements and atmospheric ment of 3-dimensional decay processes such as vortex data.23,24 Vortex data was collected from a series of bursting and Crow instability. Three of the case low-level flights in various flight configurations by a simulations (listed in bold in table 2) are presented Laser Doppler Velocimeter (LDV), an array of Mono- below. static Acoustic Vortex Sensing System (MAVSS) sensors, and a 200 ft (61 m) instrumented tower. 5 American Institute of Aeronautics and Astronautics B-757 Run-9 as a stanTdahrids paagratiincsutl awr hciacshe awlla sw saeklee-cvteodrt ebxy mthoed FelAerAs G a,b a b G r d r could compare.25 The field observations indicated a bdr a strong and persistent upwind vortex from a B-757 fly-by at 0818 MST on 25 September. The B-757 was in a where the circulation is defined as landing configuration and on a level flight path at 70 m AGL. The ambient atmosphere for the early morning G V(cid:215) dl r r flight was characterized by significant crosswinds (5.8 m/s at flight level). The lapse rate for ambient tempera- or equivalently, ture was stable, except below 20 m AGL due to the influence of the ground beginning to heat up. A strong G z dA crosswind shear was especially noted between 20 and r r 40 m AGL. where a and b are the radii of the averaging interval, and z is the axial component of vorticity. Values for As shown in Fig. 1, comparisons between field these parameters are easily determined from simulation data and TASS model results are extremely good. Both data, but less so easily from observations. observations and model results show that the vortices initially descend due to the mutual interaction of their Fig. 1 shows a comparison of the 10 m average velocity fields. However, the vertical descent of the circulation (i.e. the average circulation from r = 0 to downstream (port) vortex is suppressed as it encounters r = 10 m) for TASS data, as well as that deduced from moderate crosswind shear of opposite vorticity; and it the tower, LDV and MAVSS measurements. The eventually ascends upward with increasing lateral modeled 10 m average circulations of the two vortices separation from the upstream (starboard) vortex. The are about equal in magnitude, and bound the estimated upstream vortex descends to and remains near the circulation from field measurements. The average ground, where it translates at relatively slower speeds circulation estimated from the MAVSS sensor seems too due to the presence of weaker crosswinds. The model low, especially when compared with the LDV and tower results show several minor bounces of the upstream data. The MAVSS estimates were probably low due to vortex, resulting from the vortex interaction with the its poor resolution of the vortex core.26 ground and production of secondary vortices. Fig. 4 shows average circulation vs averaging The wind vector and potential temperature field radius at two different times from Run 9. The com- at 90 sec are shown in Figs. 2 and 3, with Fig. 2 also parison between TASS and LDV data are quite good, showing the observed positions of the wake vortices. even near the core region of the vortex. Note that potentially warmer air is carried downward with the downwash between the vortices, and potentially Comparisons in Fig. 5 from TASS data show cooler air is transported around the periphery of the that the magnitude of the 5-15 m average circulation is vortices. [Potential temperature is conserved during dry closer to that of the initial circulation processes, and thus acts as a fluid tracer.] Also evident [G (t = 0, r >> r )]. Also apparent from the normalized c in Fig. 3, is the presence of complex interactions curves in Fig. 5, the 10 m average circulation decays between the ground and the upstream vortex, including faster than the 5-15 m average circulation. the presence of an obvious secondary vortex. The purpose of the above discussion on circula- Average Circulation tion is not to advocate one parameter over the other, but In order to characterize the strength of wake to show that they can differ in magnitude and in rates of vortices, previous field investigators have defined a decay. When validating model simulations and defining parameter called average circulation.21 According to separation standards based on vortex decay rates, one reference 21, this parameter is preferable since it relates should not assume, for example, that the 10 m average to the rolling moment of an encountering aircraft and it circulation is (and decays) approximately the same as provides a more stable measurement than circulation. circulation. The average circulation is defined as 6 American Institute of Aeronautics and Astronautics IDF B-767, Runs 23 and 31 some of the 1995 cases set-up for measuring wakes Contrasting with Run 9 are two cases from B- generated in ground effect. 767 fly-bys that were flown in environments of weaker crosswind shear. In Run 23 the aircraft was in "take- Simulation results and lidar data are shown in off" configuration within a stably-stratified environment. Figs. 8 and 9 for four of the cases. The selected cases, While in Run 31 the aircraft was in "landing configura- which are summarized in table 3, represent a cross tion" within an environment of unstable stratification. section of aircraft commonly encountered at Comparison between the TASS simulations and field international airports. One of the cases (#1475) is for a data for these cases are shown in Figs. 6 and 7. MD-11 wake generated in ground effect. For run 23 (Fig. 6) there are no observations of The meteorological conditions for the selected the downstream vortex after 60 sec. In the model cases are characterized as having light crosswinds with simulation after 80 sec, the downstream vortex dimin- weak vertical shear. Since the shear was light, the ished in size and intensity, as it was coalesced within vortex pairs descend to the ground with little increase in the larger-scale circulation of the downstream vortex. separation. The crosswinds for cases #1254 and #1475 are especially light, resulting in little lateral movement In run 31 (Fig. 7), the downstream vortex was of the wakes (Fig. 9). no longer tracked after 40 sec, although the simulated downstream vortex remained intense. Comparisons between the modeled wake trajectories and lidar measurements are excellent, even In both of these events it is not known whether for case #1475, which is the MD-11 wake generated in the downstream vortex suddenly decayed or was lost by ground effect. Both the TASS simulation and lidar the LDV sensor. In each of the events, both upstream measurement show the MD-11 wake slowly rising from and downstream vortices did encounter the tower, at its generation altitude of 17.5 m to an elevation of about positions and time intervals in agreement with the model 40 m (Fig. 8), with the starboard vortex remaining in simulation. the vicinity of the flight path (Fig. 9). Unfortunately, lidar measurements of the port vortex were unavailable V. Results -- Memphis for this case and two of the other Memphis cases. The last set of TASS experiments are from the VI. Summary Memphis field experiments. The NASA-Langley sponsored field study was conducted by MIT Lincoln Two-dimensional TASS wake vortex simula- Laboratories, in November and December of 1994 and tions were compared with field measurements for a again in August 1995.27,28 The purpose of the study range of meteorological conditions and aircraft types. was to gather meteorological, wake vortex, and aircraft Successful validation of two-dimensional TASS results data at an operational airport, for use in validation of were achieved with the initialization of the appropriate wake vortex models and for direct use in the develop- observed meteorological conditions and a post roll-up ment of the AVOSS prediction system. Aircraft wake vortex system. Excellent agreement is obtained between vortex measurements were obtained with a 10.6 micron TASS predicted trajectories and measurements. Good continuous wave laser with real time identification and agreement was obtained whether the generating aircraft tracking algorithms.29 Meteorological data included: a was in landing or take-off configuration. Results from 150 ft (46 m) tower with sensors for wind velocity, the simulations indicate great sensitivity to meteorology, temperature, and humidity; a radar profiler and acoustic especially vertical wind shear. A vortex encountering a sodar for measuring winds aloft; a radio acoustic shear with opposite sense vorticity can be deflected sounding system (RASS) for providing temperature data; upwards. Circulation values predicted by TASS are and frequent rawinsonde balloon launches, for obtaining upper-bound for the observed values. The field data the vertical profiles of wind velocity and temperature. indicated a greater decay rate once the wake vortex was Aircraft data, such as weight, type, and airspeed, as one to two minutes old. However, the future inclusion well as aircraft beacon data were collected. Lidar of initial turbulence fields and the extension to three measurements were limited to arriving aircraft, with 7 American Institute of Aeronautics and Astronautics dimensions should lead to a more realistic treatment of vortex decay. Following successful validation, TASS para- metric runs are to be used to quantify the effect of weather conditions on wake-vortex transport and decay, and provide data useful for development of predictor algorithms for aircraft spacing. Table 2. Idaho Falls Validation Cases. Only those cases in bold are presented in this paper. [Dq /D z is the change in potential temperature with height, D U/D z is the change in crosswind with height, and U(Z) is the crosswind speed at the generation height] I Initial Vortex Environmental Parameters Parameters IDF Aircraft Meteor- Run # & Con- ological G ¥ S ZI Bulk Dq /D z D U/D z U(ZI) (m2/s) (m) (m) Rich- (oC per (10-2 s-1) (m/s) & date figuration Conditions ardson 100 m) # 6 727-222 stable / 320 26 79 1 8.5 5.2 5.0 9/23 landing moderate shear # 22 727-222 near- 300 26 76 .04 .1 3.0 5.4 9/23 landing neutral / moderate shear # 9 757-200 stable / 365 30 70 .5 3 4.5 5.8 9/25 landing moderate shear # 30 757-200 unstable / 360 30 70 -5.4 -0.9 0.7 2.8 9/25 landing low shear # 45 757-200 stable / 355 30 79 1.9 5.9 3.2 2.8 9/26 takeoff low shear # 7 767-200 stable / 375 38 70 0.6 7.5 6.4 4.1 9/29 landing moderate shear # 23 767-200 stable / 370 38 76 16 5 1.0 1.7 9/30 takeoff low shear # 31 767-200 unstable / 375 38 70 -15 -0.2 0.02 2.0 9/30 landing low shear 8 American Institute of Aeronautics and Astronautics Altitude vs Time Lateral Displacement vs Time 70 500 dn-LDV dn-LDV up-LDV up-LDV 60 dn-MAVS s) 400 dn-MAVS up-MAVS er up-MAVS s) 50 dunp--TTAASSSS met 300 dunp--TTAASSSS eter 40 dunp--TTOOWWEERR on ( dunp--TTOOWWEERR Altitude (m 2300 Lateral Positi 1200000 10 -100 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Time (seconds) Time (seconds) Altitude vs Lateral Displacement 10-Meter Average Circulation 70 300 dn-LDV Altitude (meters) 2345600000 dudunpnp----LLMMDDAAVVVVSS 2ge Circulation (m /sec)122505000 udududupnpnpnp-------LMMTTTTDAAOOAASSVWWVVSSSSEERR 10 dunp--TTAASSSS vera100 dn-TOWER A up-TOWER 0 50 -100 0 100 200 300 400 500 0 20 40 60 80 100 120 140 160 180 Y (meters) Time (seconds) Figure 1. Comparison of TASS results with field data for the Idaho Falls B-757 Run 9 case. The figures (left to right) are: altitude of the vortex track with time, lateral position (relative to tower) vs time, altitude vs lateral position, and 10 m circulation vs time. Upstream positions indicated by solid lines (simulation) and filled symbols (measurements), downstream positions indicated by dashed lines (simulation) and open symbols (measurements). Right triangles, squares, and circles represent LDV, MAVSS, and tower data, respectively. The average circulation estimates for the upstream and downstream vortex from MAVSS are: M and m , respectively. [Field data courtesy of Volpe National Transportation System.] 9 American Institute of Aeronautics and Astronautics
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