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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Concentration Measurements in Self-Excited, Momentum-Dominated Helium Jets

Flow structure of momentum-dominated pure helium jets discharged vertically into ambient air was investigated using high-speed rainbow schlieren deflectometry (RSD) technique. Effects of the operating parameters, i.e., Reynolds number (Re) and Richardson number (Ri), on the oscillatory behavior of the flow were examined over a range of experimental conditions. To seek the individual effect of these parameters, one of them was fixed and the other was varied with certain constraints. Measurements revealed highly periodic oscillations in the laminar region as well as high regularity in transition and turbulent regions. Maximum spectral power profiles at different axial locations indicated the oscillation amplitude increasing until the breakdown of the jet in the turbulent regime. The transition from the laminar to turbulent flow was also investigated. Fast Fourier transform analysis performed in the transition regime showed that the flow oscillates at a unique frequency, which was the same in the upstream laminar flow region. Measured deflection angle data were used in Abel inversion algorithm to construct the helium concentration fields. Instantaneous helium concentration contours revealed changes in the flow structure and evolution of vortical structures during an oscillation cycle. Temporal evolution plots of helium concentration at different axial location showed repeatable oscillations at all axial and radial locations up to the turbulent regime. A cross-correlation technique, applied to find the spatial displacements of the vortical structures, provided correlation coefficient peaks between consecutive schlieren images. Results show that the vortical structure convected and accelerated only in the axial direction.

Yildirim, Bekir Sedat↗
NASA NTRS2012

Understanding Climate Policy Data Needs. NASA Carbon Monitoring System Briefing: Characterizing Flux Uncertainty, Washington D.C., 11 January 2012

Climate policy in the United States is currently guided by public-private partnerships and actions at the local and state levels. This mitigation strategy is made up of programs that focus on energy efficiency, renewable energy, agricultural practices and implementation of technologies to reduce greenhouse gases. How will policy makers know if these strategies are working, particularly at the scales at which they are being implemented? The NASA Carbon Monitoring System (CMS) will provide information on carbon dioxide fluxes derived from observations of earth's land, ocean and atmosphere used in state of the art models describing their interactions. This new modeling system could be used to assess the impact of specific policy interventions on CO2 reductions, enabling an iterative, results-oriented policy process. In January of 2012, the CMS team held a meeting with carbon policy and decision makers in Washington DC to describe the developing modeling system to policy makers. The NASA CMS will develop pilot studies to provide information across a range of spatial scales, consider carbon storage in biomass, and improve measures of the atmospheric distribution of carbon dioxide. The pilot involves multiple institutions (four NASA centers as well as several universities) and over 20 scientists in its work. This pilot study will generate CO2 flux maps for two years using observational constraints in NASA's state-of -the-art models. Bottom-up surface flux estimates will be computed using data-constrained land and ocean models; comparison of the different techniques will provide some knowledge of uncertainty in these estimates. Ensembles of atmospheric carbon distributions will be computed using an atmospheric general circulation model (GEOS-5), with perturbations to the surface fluxes and to transport. Top-down flux estimates will be computed from observed atmospheric CO2 distributions (ACOS/GOSAT retrievals) alongside the forward-model fields, in conjunction with an inverse approach based on the CO2 model of GEOS ]Chem. The forward model ensembles will be used to build understanding of relationships among surface flux perturbations, transport uncertainty and atmospheric carbon concentration. This will help construct uncertainty estimates and information on the true spatial resolution of the top-down flux calculations. The relationship between the top-down and bottom-up flux distributions will be documented. Because the goal of NASA CMS is to be policy relevant, the scientists involved in the flux modeling pilot need to understand and be focused on the needs of the climate policy and decision making community. If policy makers are to use CMS products, they must be aware of the modeling effort and begin to design policies that can be evaluated with information. Improving estimates of carbon sequestered in forests, for example, will require information on the spatial variability of forest biomass that is far more explicit than is presently possible using only ground observations. Carbon mitigation policies being implemented by cities around the United States could be designed with the CMS data in mind, enabling sequential evaluation and subsequent improvements in incentives, structures and programs. The success of climate mitigation programs being implemented in the United States today will hang on the depth of the relationship between scientists and their policy and decision making counterparts. Ensuring that there is two-way communication between data providers and users is important for the success both of the policies and the scientific products meant to support them..

Brown, Molly E.↗
NASA NTRS2015

Constraining Black Carbon Aerosol over Asia using OMI Aerosol Absorption Optical Depth and the Adjoint of GEOS-Chem

Accurate estimates of the emissions and distribution of black carbon (BC) in the region referred to here as Southeastern Asia (70degE-l50degE, 11degS-55degN) are critical to studies of the atmospheric environment and climate change. Analysis of modeled BC concentrations compared to in situ observations indicates levels are underestimated over most of Southeast Asia when using any of four different emission inventories. We thus attempt to reduce uncertainties in BC emissions and improve BC model simulations by developing top-down, spatially resolved, estimates of BC emissions through assimilation of OMI observations of aerosol absorption optical depth (AAOD) with the GEOS-Chem model and its adjoint for April and October of 2006. Overwhelming enhancements, up to 500%, in anthropogenic BC emissions are shown after optimization over broad areas of Southeast Asia in April. In October, the optimization of anthropogenic emissions yields a slight reduction (1-5%) over India and parts of southern China, while emissions increase by 10-50% over eastern China. Observational data from in situ measurements and AERONET observations are used to evaluate the BC inversions and assess the bias between OMI and AERONET AAOD. Low biases in BC concentrations are improved or corrected in most eastern and central sites over China after optimization, while the constrained model still underestimates concentrations in Indian sites in both April and October, possibly as a. consequence of low prior emissions. Model resolution errors may contribute up to a factor of 2.5 to the underestimate of surface BC concentrations over northern India. We also compare the optimized results using different anthropogenic emission inventories and discuss the sensitivity of top-down constraints on anthropogenic emissions with respect to biomass burning emissions. In addition, the impacts of brown carbon, the formulation of the observation operator, and different a priori constraints on the optimization are investigated. Overall, despite these limitations and uncertainties, using OMI AAOD to constrain BC sources improves model representation of BC distributions, particularly over China.

Aerosols↗
NASA NTRS1987

Vector constraints on western U.S. deformation from space geodesy, neotectonics, and plate motions

The rate-of-slip vector on the San Andreas fault in central California estimated from geodetic and Holocene geological data is inconsistent with the prediction of rigid plate models such as RM2. This well-known 'San Andreas discrepancy' is diagnostic of plate deformation distributed both east of the fault in the Basin and Range and west of the fault along the California continental margin. Constraints on the integrated deformation rates across these two regions consistent with: (1) the kinematical boundary conditions imposed by the rigid plate model; (2) neotectonic and paleoseismic estimates of deformation rates; (3) ground-based geodetic measurements; and (4) rates of change observed by very long baseline interferometry along seven baselines to western U.S. sites are constructed. The space-geodetic data on Basin and Range extension taken over a 4-year interval are compatible with geological observations averaged over the Holocene; the best estimate of its integrated deformation rate, provided by the joint inversion of both data types, is 9.7 + or - 2.1 mm/yr, N 56 deg W + or - 10 deg, too small and in the wrong direction to account entirely for the San Andreas discrepancy. The integral of this deformation, estimated by subtracting the Basin and Range contribution from the discrepancy vector, requires significant right-lateral shear parallel to the San Andreas (13 + or - 5 mm/yr) and some compression perpendicular to it (9 + or - 3 mm/yr).

Minster, J. Bernard↗
NASA NTRS2013

Saturn Ring Seismology: Interpreting the Seismogram

Marley (1990) and Marley and Porco (1993) proposed that f-mode oscillations of Saturn could excite resonant density and bending waves in the inner C-ring. They hypothesized that certain wave features discovered by Rosen et al. (1991) that were not associated with known satellite resonances could be the result of such resonant interactions with the planetary oscillation modes. They also predicted that if this was the case the waves would be found to be density (and not bending) waves by Cassini and predicted the azimuthal wave number of the C-ring waves m. Employing Cassini VIMS stellar occultation data Hedman and Nicholson (2013) have now confirmed the predictions and demonstrated that at least some of the C-ring features identified by Rosen et al. are indeed likely caused by resonant oscillation modes of Saturn. Given this context we have taken a fresh look at the Saturn ring seismology. First we propose that an apparent bending wave denoted 'j' by Rosen may be a second order outer vertical resonance with the l=3, m=2 f-mode of Saturn and discuss the locations of other plausible second order resonances in the rings. Since only a handful of ring resonances have been identified, measuring even one or two additional planetary mode frequencies would substantially assist the process of inverting mode frequencies to constrain Saturn interior's structure. Using the available mode frequencies, modern inversion technique employed in stellar seismology, and a recent set of Saturn interior models we provide an initial estimation of what available mode frequencies are telling us about the interior structure of the planet. Since the f-modes are confined relatively closely to the planetary surface, most of the observed modes probe only the outermost layers of the planet that are already comparatively well understood. However the l = 2 mode does probe relatively deeply into the planet and we will discuss the potential the measurement of this mode frequency has for placing new constraints on the interior structure.

Seismogram↗
NASA NTRS1989

Computational neural learning formalisms for manipulator inverse kinematics

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints.

Gulati, Sandeep↗
NASA NTRS1976

Atmospheric temperature profiles derived through the inversion of a system of first order differential equations

Generation of vertical temperatures profiles from remotely sensed atmospheric radiance data is described as an analogous communications system. The radiative transport characteristics of the atmosphere encodes the continuous temperature profile into an 'n' element vector where 'n' is the number of channels in the satellite instrument. The temperature profile is a message transmitted from station A to station B and the link is the satellite instrument. At station B the decoder reproduces a continuous function which is the best estimate of the message encoded at station A. It is shown that the decoder must operate in a tuned mode where the parameters used in the encoder precisely determine the decoder parameters, and that the characteristics of the total message block must be given by a set of decoder constraints

Gatlin, J. A.↗
NASA NTRS2021

Conditions in the WR 140 Wind-Collision Region Revealed by the 1.083-mu m Hei Line Profile

We present spectroscopy of the P Cygni profile of the 1.083-μm He I line in the WC7+O5 colliding-wind binary (CWB) WR 140 (HD 193793), observed in 2008, before its periastron passage in 2009, and in 2016–2017, spanning the subsequent periastron passage. Both absorption and emission components showed strong variations. The variation of the absorption component as the O5 star was occulted by the wind-collision region (WCR) sets a tight constraint on its geometry. While the sightline to the O5 star traversed the WCR, the strength and breadth of the absorption component varied significantly on time-scales of days. An emission subpeak was observed on all our profiles. The variation of its radial velocity with orbital phase was shown to be consistent with formation in the WCR as it swung round the stars in their orbit. Modelling the profile gives a measure of the extent of the subpeak-forming region. In the phase range 0.93–0.99, the flux in the subpeak increased steadily, approximately inversely proportionally to the stellar separation, indicating that the shocked gas in the WCR where the line was formed was adiabatic. After periastron, the subpeak flux was anomalously strong and varied rapidly, suggesting formation in clumps downstream in the WCR. For most of the time, its flux exceeded the 2–10-keV X-ray emission, showing it to be a significant coolant of the shocked wind.

Peredur M Williams↗
NASA NTRS1984

Constraints on continuous beam models of the jet in 3C 273

The one-sidedness, 'superluminal' motion, and detailed spectra observed for 3C 273 put significant constraints on continuous beam models for the source of the extended emission in 3C 273 A. The one-sidedness of the extended emission implies that the age of the radio-frequency cloud is probably about 3-5 Myr. The 'superluminal' motion observed with VLBI constrains the bulk Lorentz factor of the jet to be more than about 10. Finally, the observed X-ray emission from the jet provides a method for deciding the question of beam composition: for a given beam power, an electron-positron beam would produce a much higher (beamed) inverse-Compton X-ray flux off extended-jet optical photons than an electron-proton beam would, thus making the observed weak jet X-ray flux a strong indicator of a proton positive component to the jet. Remaining experimental uncertainties in the case of 3C 273 make it impossible to decide the question of beam composition at present, but the next generation of experiments may make this possible for 3C 273 and other 'superluminal' objects. The above arguments have the advantage of not depending on the details of the mechanism for producing the high-energy radio-cloud electrons.

Roberts, D.↗
NASA NTRS2003

Aerodynamic Design Using Neural Networks

The design of aerodynamic components of aircraft, such as wings or engines, involves a process of obtaining the most optimal component shape that can deliver the desired level of component performance, subject to various constraints, e.g., total weight or cost, that the component must satisfy. Aerodynamic design can thus be formulated as an optimization problem that involves the minimization of an objective function subject to constraints. A new aerodynamic design optimization procedure based on neural networks and response surface methodology (RSM) incorporates the advantages of both traditional RSM and neural networks. The procedure uses a strategy, denoted parameter-based partitioning of the design space, to construct a sequence of response surfaces based on both neural networks and polynomial fits to traverse the design space in search of the optimal solution. Some desirable characteristics of the new design optimization procedure include the ability to handle a variety of design objectives, easily impose constraints, and incorporate design guidelines and rules of thumb. It provides an infrastructure for variable fidelity analysis and reduces the cost of computation by using less-expensive, lower fidelity simulations in the early stages of the design evolution. The initial or starting design can be far from optimal. The procedure is easy and economical to use in large-dimensional design space and can be used to perform design tradeoff studies rapidly. Designs involving multiple disciplines can also be optimized. Some practical applications of the design procedure that have demonstrated some of its capabilities include the inverse design of an optimal turbine airfoil starting from a generic shape and the redesign of transonic turbines to improve their unsteady aerodynamic characteristics.

Rai, Man Mohan↗
NASA NTRS1998

Helioseismic Constraints on New Solar Models from the MoSEC Code

Evolutionary solar models are computed using a new stellar evolution code, MOSEC (Modular Stellar Evolution Code). This code has been designed with carefully controlled truncation errors in order to achieve a precision which reflects the increasingly accurate determination of solar interior structure by helioseismology. A series of models is constructed to investigate the effects of the choice of equation of state (OPAL or MHD-E, the latter being a version of the MHD equation of state recalculated by the author), the inclusion of helium and heavy-element settling and diffusion, and the inclusion of a simple model of mixing associated with the solar tachocline. The neutrino flux predictions are discussed, while the sound speed of the computed models is compared to that of the sun via the latest inversion of SOI-NMI p-mode frequency data. The comparison between models calculated with the OPAL and MHD-E equations of state is particularly interesting because the MHD-E equation of state includes relativistic effects for the electrons, whereas neither MHD nor OPAL do. This has a significant effect on the sound speed of the computed model, worsening the agreement with the solar sound speed. Using the OPAL equation of state and including the settling and diffusion of helium and heavy elements produces agreement in sound speed with the helioseismic results to within about +.-0.2%; the inclusion of mixing slightly improves the agreement.

Elliott, J. R.↗
NASA NTRS1994

Super-Eddington radiation transfer in soft gamma repeaters

Bursts from soft gamma repeaters (SGRs) have been shown to be super-Eddington by a factor of 1000 and have been persuasively associated with compact objects. Super-Eddington radiation transfer on the surface of a strongly magnetic (greater than or equal to 10(exp 13) G) neutron star is studied and related to the observational constraints on SGRs. In strong magnetic fields, Thompson scattering is suppressed in one polarization state, so super-Eddington fluxes can be radiated while the plasma remains in hydrostatic equilibrium. We discuss a model which offers a somewhat natural explanation for the observation that the energy spectra of bursts with varying intensity are similar. The radiation produced is found to be linearly polarized to one part in 1000 in a direction determined by the local magnetic field, and intensity variations between bursts are understood as a change in the radiating area on the source. The net polarization is inversely correlated with burst intensity. Further, it is shown that for radiation transfer calculations in limit of superstrong magnetic fields, it is sufficient to solve the radiation transfer for the low opacity state rather than the coupled equations for both. With this approximation, standard stellar atmosphere techniques are utilized to calculate the model energy spectrum.

Ulmer, Andrew↗
NASA NTRS2001

Constraints on Variability of Brightness and Surface Magnetism on Time Scales of Decades to Centuries in the Sun and Sun-Like Stars: A Source of Potential Terrestrial Climate Variability

These four points summarize our work to date. (1) Conciliation of solar and stellar photometric variability. Previous research by us and colleagues suggested that the Sun might at present be showing unusually low photometric variability compared to other sun-like stars. Those early results would question the suitability of the technique of using sun-like stars as proxies for solar irradiance change on time scales of decades to centuries. However, our results indicate the contrary: the Sun's observed short-term (seasonal) and longterm (year-to-year) brightness variations closely agree with observed brightness variations in stars of similar mass and age. (2) We have demonstrated an inverse correlation between the global temperature of the terrestrial lower troposphere, inferred from the NASA Microwave Sounding Unit (MSU) radiometers, and the total area of the Sun covered by coronal holes from January 1979 to present (up to May 2000). Variable fluxes of either solar charged particles or cosmic rays, or both, may influence the terrestrial tropospheric temperature. The geographical pattern of the correlation is consistent with our interpretation of an extra-terrestrial charged particle forcing. (3) Possible climate mechanism amplifying the impact of solar ultraviolet irradiance variations. The key points of our proposed climate hypersensitivity mechanism are: (a) The Sun is more variable in the UV (ultraviolet) than in the visible. However, the increased UV irradiance is mainly absorbed in the lower stratosphere/upper troposphere rather than at the surface. (b) Absorption in the stratosphere raises the temperature moderately around the vicinity of the tropopause, and tends to stabilize the atmosphere against vertical convective/diffusive transport, thus decreasing the flux of heat and moisture carried upward from surface. (c) The decrease in the upward convection of heat and moisture tends to raise the surface temperature because a drier upper atmosphere becomes less cloudy, which in turn allows more solar radiation to reach the Earth's surface. (4) Natural variability in an ocean-atmosphere climate model. We use a 14-region, 6-layer, global thermo-hydrodynamic ocean-atmosphere model to study natural climate variability. All the numerical experiments were performed with no change in the prescribed external boundary conditions (except for the seasonal cycle of the Sun's tilt angle). Therefore, the observed inter-annual variability is of an internal kind. The model results are helpful toward the understanding of the role of nonlinearity in climate change. We have demonstrated a range of possible climate behaviors using our newly developed ocean-atmosphere model. These include climate configurations with no interannual variability, with multi-year periodicities, with continuous chaos, or with chaotically occuring transitions between two discrete substrates. These possible modes of climate behavior are all possible for the real climate, as well as the model. We have shown that small temporary climate influences can trigger shifts both in the mean climate, and among these different types of behavior. Such shifts are not only theoretically plausible, as shown here and elsewhere; they are omnipresent in the climate record on time scales from several years to the age of the Earth. This has two apparently opposite implications for the possibility of anthropogenic global warming. First, any warming which might occur as a result of human influence would be only a fraction of the small-to-large unpredictable natural changes and changes which result from other external causes. On the other hand, small temporary influences such as human influence do have the potential of causing large permanent shifts in mean climate and interannual variability.

Baliunas, Sallie L.↗
NASA NTRS1978

Equation of state fits to the lower mantle and outer core

The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data. Homogeneous regions are found at radii between 5125 and 4825 km, 4600 and 3850 km, and 3200 and 2200 km. The lower mantle and outer core are inhomogeneous on the whole and are only homogeneous in the above local regions. Finite-strain and atomistic equations of state are fit to the homogeneous regions. The apparent convergence of the finite-strain relations is examined to judge their applicability to a given region. In some cases the observed pressure derivatives of the elastic moduli are used as additional constraints. The effect of minor deviations from adiabaticity on the extrapolations is also considered. An ensemble of zero-pressure values of the density and seismic velocities are found for these regions. The range of extrapolated values from these several approaches provides a measure of uncertainties involved.

Butler, R.↗
NASA NTRS1985

The deep structure of lunar basins - Implications for basin formation and modification

Models for the crustal structure in the vicinity of nine impact basins, from an inversion of gravity and topographic data from the lunar nearside are presented. The models display a low-density nonmare crustal layer and a mare basalt layer, both of variable thicknesses. Assuming that topography in mare areas is isostatically compensated before the emplacement of mare basalts and that compensation of mare basalt units may be neglected, a decomposition of the gravity anomaly into contributions from Moho relief and mare fill is permitted. Minimum values for mare basalt thicknesses are obtained but because mare basalts and mantle material are similar in density, the thicknesses of the nonmare crust are estimated. An important constraint is the crustal thickness inferred from the Apollo 12 and 14 landing sites from seismic observations. The crustal thickness model indicates that the crust is thinner beneath each of the major nearside basins than in surrounding areas. New bounds on the volume of material ejected from each basin are derived. The geological implications of structural differences among basins for the processes of basin formation and modification are evaluated as functions of time on the moon.

Bratt, S. R.↗
NASA NTRS2021

Conditions in the WR 140 Wind-collision Region Revealed by the 1.083-um He I Line Profile

We present spectroscopy of the P Cygni profile of the 1.083-μm He i line in the WC7 + O5 colliding-wind binary (CWB) WR140 (HD 193793), observed in 2008, before its periastron passage in 2009, and in 2016–17, spanning the subsequent periastron passage. Both absorption and emission components showed strong variations. The variation of the absorption component as the O5 star was occulted by the wind-collision region (WCR) sets a tight constraint on its geometry. While the sightline to the O5 star traversed the WCR, the strength and breadth of the absorption component varied significantly on time-scales of days. An emission sub-peak was observed on all our profiles. The variation of its radial velocity with orbital phase was shown to be consistent with formation in the WCR as it swung round the stars in their orbit. Modelling the profile gave a measure of the extent of the sub-peak forming region. In the phase range 0.93–0.99, the flux in the sub-peak increased steadily, approximately inversely proportionally to the stellar separation, indicating that the shocked gas in the WCR where the line was formed was adiabatic. After periastron, the sub-peak flux was anomalously strong and varied rapidly, suggesting formation in clumps down-stream in the WCR. For most of the time, its flux exceeded the 2–10-keV X-ray emission, showing it to be a significant coolant of the shocked wind.

Peredur M Williams↗
NASA NTRS1972

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.

Wiggins, R. A.↗
NASA NTRS2008

Simulation of Ground Winds Time Series for the NASA Crew Launch Vehicle (CLV)

Simulation of wind time series based on power spectrum density (PSD) and spectral coherence models for ground wind turbulence is described. The wind models, originally developed for the Shuttle program, are based on wind measurements at the NASA 150-m meteorological tower at Cape Canaveral, FL. The current application is for the design and/or protection of the CLV from wind effects during on-pad exposure during periods from as long as days prior to launch, to seconds or minutes just prior to launch and seconds after launch. The evaluation of vehicle response to wind will influence the design and operation of constraint systems for support of the on-pad vehicle. Longitudinal and lateral wind component time series are simulated at critical vehicle locations. The PSD model for wind turbulence is a function of mean wind speed, elevation and temporal frequency. Integration of the PSD equation over a selected frequency range yields the variance of the time series to be simulated. The square root of the PSD defines a low-pass filter that is applied to adjust the components of the Fast Fourier Transform (FFT) of Gaussian white noise. The first simulated time series near the top of the launch vehicle is the inverse transform of the adjusted FFT. Simulation of the wind component time series at the nearest adjacent location (and all other succeeding next nearest locations) is based on a model for the coherence between winds at two locations as a function of frequency and separation distance, where the adjacent locations are separated vertically and/or horizontally. The coherence function is used to calculate a coherence weighted FFT of the wind at the next nearest location, given the FFT of the simulated time series at the previous location and the essentially incoherent FFT of the wind at the selected location derived a priori from the PSD model. The simulated time series at each adjacent location is the inverse Fourier transform of the coherence weighted FFT. For a selected design case, the equations, the process and the simulated time series at multiple vehicle stations are presented.

Adelfang, Stanley I.↗