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NASA NTRS1981

A satellite investigation of energy flux and inferred potential drop in auroral electron energy spectra

The relationship between auroral electron energy flux and the inferred accelerating potential drop for accelerated Maxwellian distributions is investigated on the basis of Atmospheric Explorer D spectral measurements. An analytical approximation for the total downward energy flux carried by an isotropic Maxwellian electron population accelerated by a field-aligned electrostatic potential drop is derived which is valid for values of the electron energy/characteristic accelerated Maxwellian distribution energy which are less than the difference between the ratio of the magnetic field strengths at the altitude of observation and the altitude of potential drop, and unity. Data from the Low Energy Electron Experiment on board AE D obtained on both the dayside and the nightside during periods of significant inverted-V type electron precipitation shows that the 455 energy spectra considered, 160 of them, obtained between 60 and 85 deg invariant latitude, could be fit to accelerated Maxwellian distributions. The 160 Maxwellian spectra are then shown to be in agreement with the predictions of the accelerated Maxwellian model. Finally, analysis of individual spectra suggests that the altitude of the inferred potential drop is at a maximum near the center of the inverted-V structures.

Menietti, J. D.↗

NASA NTRS1995

Experimental Investigation of Textile Composite Materials Using Moire Interferometry

The viability as an efficient aircraft material of advanced textile composites is currently being addressed in the NASA Advanced Composites Technology (ACT) Program. One of the expected milestones of the program is to develop standard test methods for these complex material systems. Current test methods for laminated composites may not be optimum for textile composites, since the architecture of the textile induces nonuniform deformation characteristics on the scale of the smallest repeating unit of the architecture. The smallest repeating unit, also called the unit cell, is often larger than the strain gages used for testing of tape composites. As a result, extending laminated composite test practices to textiles can often lead to pronounced scatter in material property measurements. It has been speculated that the fiber architectures produce significant surface strain nonuniformities, however, the magnitudes were not well understood. Moire interferometry, characterized by full-field information, high displacement sensitivity, and high spatial resolution, is well suited to document the surface strain on textile composites. Studies at the NASA Langley Research Center on a variety of textile architectures including 2-D braids and 3-D weaves, has evidenced the merits of using moire interferometry to guide in test method development for textile composites. Moire was used to support tensile testing by validating instrumentation practices and documenting damage mechanisms. It was used to validate shear test methods by mapping the full-field deformation of shear specimens. Moire was used to validate open hole tension experiments to determine the strain concentration and compare then to numeric predictions. It was used for through-the-thickness tensile strength test method development, to verify capabilities for testing of both 2-D and 3-D material systems. For all of these examples, moire interferometry provided vision so that test methods could be developed with less speculation and more documentation.

Ifju, Peter G.↗

NASA NTRS1984

Inlet flow field investigation. Part 1: Transonic flow field survey

A wind tunnel investigation was conducted to determine the local inlet flow field characteristics of an advanced tactical supersonic cruise airplane. A data base for the development and validation of analytical codes directed at the analysis of inlet flow fields for advanced supersonic airplanes was established. Testing was conducted at the NASA-Langley 16-foot Transonic Tunnel at freestream Mach numbers of 0.6 to 1.20 and angles of attack from 0.0 to 10.0 degrees. Inlet flow field surveys were made at locations representative of wing (upper and lower surface) and forebody mounted inlet concepts. Results are presented in the form of local inlet flow field angle of attack, sideflow angle, and Mach number contours. Wing surface pressure distributions supplement the flow field data.

Yetter, J. A.↗

NASA NTRS2011

An Investigation Into HPLC Data Quality Problems

This report summarizes the analyses and results produced by a five-member investigative team of Government, university, and industry experts, established by NASA HQ. The team examined data quality problems associated with high performance liquid chromatography (HPLC) analyses of pigment concentrations in seawater samples produced by the San Diego State University (SDSU) Center for Hydro-Optics and Remote Sensing (CHORS). This report shows CHORS did not validate the methods used before placing them into service to analyze field samples for NASA principal investigators (PIs), even though the HPLC literature contained easily accessible method validation procedures, and the importance of implementing them, more than a decade ago. In addition, there were so many sources of significant variance in the CHORS methodologies, that the HPLC system rarely operated within performance criteria capable of producing the requisite data quality. It is the recommendation of the investigative team to a) not correct the data, b) make all the data that was temporarily sequestered available for scientific use, and c) label the affected data with an appropriate warning, e.g., "These data are not validated and should not be used as the sole basis for a scientific result, conclusion, or hypothesis--independent corroborating evidence is required."

Hooker, Stanford B.↗

NASA NTRS1992

SeaWiFS calibration and validation plan, volume 3

The Sea-viewing Wide Field-of-view Sensor (SeaWiFS) will be the first ocean-color satellite since the Nimbus-7 Coastal Zone Color Scanner (CZCS), which ceased operation in 1986. Unlike the CZCS, which was designed as a proof-of-concept experiment, SeaWiFS will provide routine global coverage every 2 days and is designed to provide estimates of photosynthetic concentrations of sufficient accuracy for use in quantitative studies of the ocean's primary productivity and biogeochemistry. A review of the CZCS mission is included that describes that data set's limitations and provides justification for a comprehensive SeaWiFS calibration and validation program. To accomplish the SeaWiFS scientific objectives, the sensor's calibration must be constantly monitored, and robust atmospheric corrections and bio-optical algorithms must be developed. The plan incorporates a multi-faceted approach to sensor calibration using a combination of vicarious (based on in situ observations) and onboard calibration techniques. Because of budget constraints and the limited availability of ship resources, the development of the operational algorithms (atmospheric and bio-optical) will rely heavily on collaborations with the Earth Observing System (EOS), the Moderate Resolution Imaging Spectrometer (MODIS) oceans team, and projects sponsored by other agencies, e.g., the U.S. Navy and the National Science Foundation (NSF). Other elements of the plan include the routine quality control of input ancillary data (e.g., surface wind, surface pressure, ozone concentration, etc.) used in the processing and verification of the level-0 (raw) data to level-1 (calibrated radiances), level-2 (derived products), and level-3 (gridded and averaged derived data) products.

Hooker, Stanford B.↗

NASA NTRS1994

Directional and polarimetric effects in the optical domain

Papers focused on land surface, atmospheric, and ocean properties are reported. Specific comments pertaining to polarization, models and inversion, and measurements, are given. Recommendations are: continued research into the application potential of the BRDF (Bidirectional Reflectance Distribution Function) and polarization properties of ground surface and atmospheric targets; three dimensional models, which account for the statistical behavior of remotely sensed data, should be extended and inverted in order to support analysis of data potentially covering rolling terrain such that pixels represent heterogeneous mixtures of surface cover types and project ground footprints with sizes between 10 to 6 km, the ground pixel sizes of planned future sensors; available reflectance models should be further validated by means of multi dimensional (directional, spectral, temporal) field data and existing models should be intercompared in more depth to evaluate their performance and limitations; existing methods for model inversion should be validated in more depth in order to quantify the practical limitations and the expected accuracy of the parameters retrieved and new approaches should be developed based upon apriori knowledge of plant canopy development and spectral BRDF properties; there is a need to establish a protocol of validation and intercomparison of the indices and compositing techniques which have been proposed during these last years.

Vanderbilt, V. C.↗

NASA NTRS2001

Bio-Optical Measurements at Ocean Boundaries in Support of SIMBIOS

The equatorial Pacific is a major component of global biogeochemical cycles, due to upwelling that occurs from the coast of South America to beyond 180 deg. This upwelling has significant implications for global CO2 fluxes, as well as primary and secondary production. In addition, this region of the world's oceans represents a large oceanic province over which validation data for Sea-Viewing Wide Field-of-view Sensor (SeaWiFS) are necessary. This project consists of a mooring program and supporting cruise-based measurements aimed at quantifying the spectrum of biological and chemical variability in the equatorial Pacific and obtaining validation data for SeaWiFS. The project has the following general objectives: (1) to understand the relationships between physical forcing, primary production, nutrient supply and the exchange of carbon dioxide between ocean and atmosphere in the equatorial Pacific; (2) to describe the biological and chemical responses to climate and ocean variability; (3) to describe the spatial, seasonal and inter-annual variability in near surface plant pigments, primary production, carbon dioxide and nutrient distributions; and (4) to obtain near real-time bio-optical measurements for validation of SeaWiFS and subsequent ocean color sensors.

Chavez, Francisco P.↗

NASA NTRS1999

Development of Optical Diagnostic Techniques for Microgravity Materials Processing

Materials processing including crystal growth, either under a gravity environment on ground or a microgravity environment in space, involves complicated phenomena of fluid motions in gas or liquid phases as well as interaction of various species. To obtain important physical insight, it is very necessary to provide gross-field optical diagnostics for monitoring various physical properties. Materials processing inhibits easy access by ordinary instruments and thus characterizing gross-field physical properties is very challenging. Typical properties of importance can be fluid velocity, temperature, and species concentration for fluids, and surface topology and defects for solids. Observing surface grow rate during crystal growth is also important. Material microstructures, i.e., integrity of crystal structures, is strongly influenced by the existence of thermally-induced flow as well as local nucleation of particles during solidification, which may act in many detrimental ways. In both ground-based and microgravity experiments, the nature of product property changes resulting from three-dimensional fluid or particle motions need be characterized. Gross-field diagnostics is thus required to identify their effects on product defects and process deficiencies. The quantitative visualization techniques can also be used for validation of numerical modeling. For optical nonintrusive gross-field diagnostic techniques, two approaches were developed as summer projects. One optical approach allows us to provide information of species concentration and temperature for monitoring in real time. The other approach, that is, the concept which is formulated for detection of surface topography measurement can provide unprecedented spatial resolution during crystal growth.

Cha, Soyoung Stephen↗

NASA NTRS2003

Magnetic Control of Solutal Buoyancy Driven Convection

Volumetric forces resulting from local density variations and gravitational acceleration cause buoyancy induced convective motion in melts and solutions. Solutal buoyancy is a result of concentration differences in an otherwise isothermal fluid. If the fluid also exhibits variations in magnetic susceptibility with concentration then convection control by external magnetic fields can be hypothesized. Magnetic control of thermal buoyancy induced convection in ferrofluids (dispersions of ferromagnetic particles in a carrier fluid) and paramagnetic fluids have been demonstrated. Here we show the nature of magnetic control of solutal buoyancy driven convection of a paramagnetic fluid, an aqueous solution of Manganese Chloride hydrate. We predict the critical magnetic field required for balancing gravitational solutal buoyancy driven convection and validate it through a simple experiment. We demonstrate that gravity driven flow can be completely reversed by a magnetic field but the exact cancellation of the flow is not possible. This is because the phenomenon is unstable. The technique can be applied to crystal growth processes in order to reduce convection and to heat exchanger devices for enhancing convection. The method can also be applied to impose a desired g-level in reduced gravity applications.

Ramachandran, N.↗

NASA NTRS1977

Utility of correlation techniques in gravity and magnetic interpretation

Internal correspondence uses Poisson's Theorem in a moving-window linear regression analysis between the anomalous first vertical derivative of gravity and total magnetic field reduced to the pole. The regression parameters provide critical information on source characteristics. The correlation coefficient indicates the strength of the relation between magnetics and gravity. Slope value gives delta j/delta sigma estimates of the anomalous source. The intercept furnishes information on anomaly interference. Cluster analysis consists of the classification of subsets of data into groups of similarity based on correlation of selected characteristics of the anomalies. Model studies are used to illustrate implementation and interpretation procedures of these methods, particularly internal correspondence. Analysis of the results of applying these methods to data from the midcontinent and a transcontinental profile shows they can be useful in identifying crustal provinces, providing information on horizontal and vertical variations of physical properties over province size zones, validating long wavelength anomalies, and isolating geomagnetic field removal problems.

Chandler, V. W.↗

NASA NTRS2013

A Comparison of Foliage Profiles in the Sierra National Forest Obtained with a Full-Waveform Under-Canopy EVI Lidar System with the Foliage Profiles Obtained with an Airborne Full-Waveform LVIS Lidar System

Foliage profiles retrieved froma scanning, terrestrial, near-infrared (1064 nm), full-waveformlidar, the Echidna Validation Instrument (EVI), agree well with those obtained from an airborne, near-infrared, full-waveform, large footprint lidar, the Lidar Vegetation Imaging Sensor (LVIS). We conducted trials at 5 plots within a conifer stand at Sierra National Forest in August, 2008. Foliage profiles retrieved from these two lidar systems are closely correlated (e.g., r = 0.987 at 100 mhorizontal distances) at large spatial coverage while they differ significantly at small spatial coverage, indicating the apparent scanning perspective effect on foliage profile retrievals. Alsowe noted the obvious effects of local topography on foliage profile retrievals, particularly on the topmost height retrievals. With a fine spatial resolution and a small beam size, terrestrial lidar systems complement the strengths of the airborne lidars by making a detailed characterization of the crowns from a small field site, and thereby serving as a validation tool and providing localized tuning information for future airborne and spaceborne lidar missions.

Full-waveform↗

NASA NTRS2002

Evaluation of Methods to Estimate the Surface Downwelling Longwave Flux during Arctic Winter

Surface longwave radiation fluxes dominate the energy budget of nighttime polar regions, yet little is known about the relative accuracy of existing satellite-based techniques to estimate this parameter. We compare eight methods to estimate the downwelling longwave radiation flux and to validate their performance with measurements from two field programs in thc Arctic: the Coordinated Eastern Arctic Experiment (CEAREX ) conducted in the Barents Sea during the autumn and winter of 1988, and the Lead Experiment performed in the Beaufort Sea in the spring of 1992. Five of the eight methods were developed for satellite-derived quantities, and three are simple parameterizations based on surface observations. All of the algorithms require information about cloud fraction, which is provided from the NASA-NOAA Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) polar pathfinder dataset (Path-P): some techniques ingest temperature and moisture profiles (also from Path-P): one-half of the methods assume that clouds are opaque and have a constant geometric thickness of 50 hPa, and three include no thickness information whatsoever. With a somewhat limited validation dataset, the following primary conclusions result: (1) all methods exhibit approximately the same correlations with measurements and rms differences, but the biases range from -34 W sq m (16% of the mean) to nearly 0; (2) the error analysis described here indicates that the assumption of a 50-hPa cloud thickness is too thin by a factor of 2 on average in polar nighttime conditions; (3) cloud-overlap techniques. which effectively increase mean cloud thickness, significantly improve the results; (4) simple Arctic-specific parameterizations performed poorly, probably because they were developed with surface-observed cloud fractions; and (5) the single algorithm that includes an estimate of cloud thickness exhibits the smallest differences from observations.

Chiacchio, Marc↗

NASA NTRS2020

An Introduction to the NASA GMAO Coupled Atmosphere-Ocean System - GEOS-S2S Version 3

Recently NASA's Global Modeling and Assimilation Office (GMAO) has developed a new Subseasonal to Seasonal Prediction system Version 3 (GEOS-S2S-3). This upgrade replaces the GEOS-S2S-2 which is NASA's current contribution to the North American Multi-Model Experiment seasonal prediction project (Kirtman et al., 2014). The main improvements for our S2S-3 system include 1) a higher resolution MOM5 (Griffies et al., 2005) ocean model (now 0.25o x 0.25o x 50 layers), 2) an improved atmospheric/ocean interface layer (Akella and Suarez, 2018), and 3) assimilation of a long-track satellite salinity into the ocean model (Hackert et al, 2019). Atmospheric forcing is provided by the NASA MERRA-2 reanalysis (Gelaro et al., 2017). Initialization for the ocean relies on the GMAO ocean reanalysis system which assimilates all available in situ temperature and salinity, satellite sea surface salinity, and sea level using the Local Ensemble Transform Kalman Filter (LETKF) implementation of (Penny et al., 2013) on a 5 day assimilation cycle with 20 fixed ensemble members.In this presentation, we will authenticate our new S2S-3 ocean reanalysis using standard GODAE validation metrics. For example, we will compare gridded fields of mean and standard deviation of the ocean reanalysis versus observed fields. We will show correlation/RMS of model versus observations and temperature and salinity mean profiles for the various basins and latitude bands. Basin-scale volume transports, such as the Atlantic Meridional Overturning Circulation and the Indonesian Throughflow will be validated. Equatorial ocean waves will be compared by decomposing sea level into Kelvin and Rossby components. For each of these metrics, we plan to validate the results and then compare our new S2S-3 against the current production version, S2S-2. Finally, we will compare 9-month seasonal forecasts initialized from these two systems for the tropical Pacific NINO3.4 region over the period 1981-present.

Molod, Andrea↗

NASA NTRS1999

High-Resolution Mapping of Lunar Crustal Magnetic Fields: Correlations with Albedo Markings of the Reiner Gamma Class

During the last eight months of the Lunar Prospector mission (December 1999-July 1999), the spacecraft was placed in a relatively low-altitude (15-30-km perapsis), near-polar orbit that allowed high-resolution mapping of crustal magnetic fields. We report here initial studies of the correlation of locally strong magnetic anomalies with unusual, swirl-like albedo markings of the Reiner Gamma class. Based on this correlation, which is known from earlier studies of Apollo subsatellite magnetometer data, it has been proposed that the swirls represent regions whose higher albedos have been preserved via deflection of the solar-wind ion bombardment by strong crustal fields. This model in turn depends on the hypothesis that solar-wind implanted H is at least one component of the process that optically matures exposed silicate surfaces in the inner solar system . Specifically, it is hypothesized that implanted H acts as an effective reducing agent to enhance the rate of production of nanophase metallic Fe particles from preexisting silicates during micrometeoroid impacts. According to the model, the curvilinear shapes of these albedo markings are caused, at least in part, by the geometry of ion deflections in a magnetic field. The improved resolution and coverage of the Prospector data allow more detailed mapping of the fields, especially on the lunar farside. This permits a more quantitative test of whether all albedo markings of this class are associated with strong local magnetic fields.Only if the latter condition is met can the solar-wind deflection hypothesis he valid. The basic procedure for mapping crustal magnetic fields using Lunar Prospector magnetometer data follows that developed for analysis of Apollo subsatellite magnetometer data. The specific mapping steps are (1) selection of mission time intervals suitable for mapping crustal fields; these are limited essentially either to times when the Moon is in a lobe of the geomagnetic tail or to times when the Moon is in the solar wind but the spacecraft is in the lunar wake; the data are transformed to a radial, east, and north coordinate system with measurements given as a function of spacecraft latitude, longitude, and altitude; (2) visual editing of individual orbit segments selected for minimal external field disturbances; (3) minimization of remaining low-frequency external fields for individual orbit data segments by quadratic detrending; and (4) two-dimensional filtering of individual orbit segments to produce a vector field map along the slightly curved surface defined by the spacecraft altitude; maps of the three field components (radial, east, and north), the field magnitude, and the spacecraft altitude are constructed. For data obtained at low to middle latitudes, the horizontal resolution of the field maps is limited by the orbit-track separation (about 30 km at the equator). Maps of the field magnitude have been constructed within limited selenographic regions based mainly on data acquired in March, April, and May of 1999. This was a time period when the orbit plane was nearly aligned with the Sun-Moon line so that field mapping was possible at times when the Moon was in the solar wind as well as when the Moon was in the geomagnetic tail. Most of the coverage is across the lunar farside. However, a shows an example of a field map produced from solar-wind wake data for a region including Reiner Gamm on western Oceanus Procellarum (location: 58.5W, 7.5N). The contour interval is 3 nT and the mean spacecraft altitude is 18 km to within the accuracy allowed by the resolution of the map (30 km or about 1 deg.); strong magnetic anomalies correlate closely with swirl locations. Individual orbit profiles (whose resolution along the orbit track is comparable to the spacecraft altitude of 18 km) also demonstrate a good correlation of field magnitude with surface albedo. In order to investigate the correlation of magnetic fields with the location of swirl features, we have reexamined available lunar imagery (Lunar Orbiter, Apollo, and Clementine) to identify and map swirl locations within regions where swirls have previously been mapped. In these images, swirls were distinguished from other high-albedo features such as crater rays by their curvilinear shapes and increased visibility in forward-scattered light. Digital maps of swirls identified by all available imagery were then superposed on maps of the field magnitude at the spacecraft altitude. Based upon analysis of these composite magnetic/geologic maps, we draw the preliminary conclusion that swirl features are associated with magnetic anomalies revealed by Lunar Prospector. Detailed maps of these swirl features are currently being constructed for the magnetically strong regions antipodal to the Imbrium, Serenitatis, and Crisium Basins. Additional information contained in the original,

Hood, L. L.↗

NASA NTRS1990

Application of CFD to sonic boom near and mid flow-field prediction

A 3-D parabolized Navier-Stokes (PNS) code was used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction.

Cheung, Samson H.↗

NASA NTRS2015

Atmospheric Research 2014 Technical Highlights

Atmospheric research in the Earth Sciences Division (610) consists of research and technology development programs dedicated to advancing knowledge and understanding of the atmosphere and its interaction with the climate of Earth. The Division's goals are to improve understanding of the dynamics and physical properties of precipitation, clouds, and aerosols; atmospheric chemistry, including the role of natural and anthropogenic trace species on the ozone balance in the stratosphere and the troposphere; and radiative properties of Earth's atmosphere and the influence of solar variability on the Earth's climate. Major research activities are carried out in the Mesoscale Atmospheric Processes Laboratory, the Climate and Radiation Laboratory, the Atmospheric Chemistry and Dynamics Laboratory, and the Wallops Field Support Office. The overall scope of the research covers an end-to-end process, starting with the identification of scientific problems, leading to observation requirements for remote-sensing platforms, technology and retrieval algorithm development; followed by flight projects and satellite missions; and eventually, resulting in data processing, analyses of measurements, and dissemination from flight projects and missions. Instrument scientists conceive, design, develop, and implement ultraviolet, infrared, optical, radar, laser, and lidar technology to remotely sense the atmosphere. Members of the various Laboratories conduct field measurements for satellite sensor calibration and data validation, and carry out numerous modeling activities. These modeling activities include climate model simulations, modeling the chemistry and transport of trace species on regional-to-global scales, cloud resolving models, and developing the next-generation Earth system models. Satellite missions, field campaigns, peer-reviewed publications, and successful proposals are essential at every stage of the research process to meeting our goals and maintaining leadership of the Earth Sciences Division in atmospheric science research. Figure 1.1 shows the 20-year record of peer-reviewed publications and proposals among the various Laboratories. This data shows that the scientific work being conducted in the Laboratories is competitive with the work being done elsewhere in universities and other government agencies. The office of Deputy Director for Atmospheric Research will strive to maintain this record by rigorously monitoring and promoting quality while emphasizing coordination and integration among atmospheric disciplines. Also, an appropriate balance will be maintained between the scientists' responsibility for large collaborative projects and missions and their need to carry out active science research as a principal investigator. This balance allows members of the Laboratories to improve their scientific credentials, and develop leadership potentials. Interdisciplinary research is carried out in collaboration with other laboratories and research groups within the Earth Sciences Division, across the Sciences and Exploration Directorate, and with partners in universities and other government agencies. Members of the Laboratories interact with the general public to support a wide range of interests in the atmospheric sciences. Among other activities, the Laboratories raise the public's awareness of atmospheric science by presenting public lectures and demonstrations, by making scientific data available to wide audiences, by teaching, and by mentoring students and teachers. The Atmosphere Laboratories make substantial efforts to attract and recruit new scientists to the various areas of atmospheric research. We strongly encourage the establishment of partnerships with Federal and state agencies that have operational responsibilities to promote the societal application of our science products. This report describes our role in NASA's mission, provides highlights of our research scope and activities, and summarizes our scientists' major accomplishments during calendar year 2014. The composition of the organization is shown in Figure 1.2 for each code. This report is published in a printed version with an electronic version on our atmospheres Web site, http://atmospheres.gsfc.nasa.gov/.

Technical↗

NASA NTRS2017

Atmospheric Research 2016 Technical Highlights

Atmospheric↗

NASA NTRS1996

Theoretical Basis for Finite Difference Extrapolation of Sonic Boom Signatures

Calculation of sonic boom signatures for aircraft has traditionally followed the methods of Whitham' and Walkden. The wave disturbance generated by the vehicle is obtained by area rule linearized supersonic flow methods, which yield a locally axisymmetric asymptotic solution. This solution is acoustic in nature, i.e., first order in disturbance quantities, and corresponds to ray acoustics. Cumulative nonlinear distortion of the signature is incorporated by using this solution to adjust propagation speed to first order, thus yielding a solution second order in disturbance quantities. The effects of atmospheric gradients are treated by Blokhintzov's method of geometrical acoustics. Both nonlinear signature evolution and ray tracing are applied as if the pressure field very close to the vehicle were actually that given by the source term (the 'F-function') of the asymptotic linearized flow solution. The viewpoint is thus that the flow solution exists at a small radius near the vehicle, and may be treated as an input to an extrapolation procedure consisting of ray tracing and nonlinear aging. The F-function is often regarded as a representation of a near-field pressure signature, and it is common for computational implementations to treat it interchangeably with the pressure signature. There is a 'matching radius' between the source function and the subsequent propagation extrapolation. This viewpoint has been supported by wind tunnel tests of simple models, and very typically yields correct results for actual flight vehicles. The assumption that the F-function and near-field signature are interchangeable is generally not correct. The flowfield of a vehicle which is not axisymmetric contains crossflow components which are very significant at small radii and less so at larger distances. From an acoustical viewpoint, the crossflow is equivalent to source diffraction portions of the wave field. Use of the F-function as a near field signature effectively assumes that the diminution of the crossflow/diffraction component may be applied all at once at the matching radius noted above. This approximation, though not rigorously validated, is responsible for the usual correct far-field results. On the other hand, if an actual near-field signature (either from wind tunnel or CFD data) is used at a starting point rather than one based on th effective source distribution, the predicted far-field signature is generally wrong.

Plotkin, Kenneth J.↗