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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS2012

Accelerated Creep Testing of High Strength Aramid Webbing

A series of preliminary accelerated creep tests were performed on four variants of 12K and 24K lbf rated Vectran webbing to help develop an accelerated creep test methodology and analysis capability for high strength aramid webbings. The variants included pristine, aged, folded and stitched samples. This class of webbings is used in the restraint layer of habitable, inflatable space structures, for which the lifetime properties are currently not well characterized. The Stepped Isothermal Method was used to accelerate the creep life of the webbings and a novel stereo photogrammetry system was used to measure the full-field strains. A custom MATLAB code is described, and used to reduce the strain data to produce master creep curves for the test samples. Initial results show good correlation between replicates; however, it is clear that a larger number of samples are needed to build confidence in the consistency of the results. It is noted that local fiber breaks affect the creep response in a similar manner to increasing the load, thus raising the creep rate and reducing the time to creep failure. The stitched webbings produced the highest variance between replicates, due to the combination of higher local stresses and thread-on-fiber damage. Large variability in the strength of the webbings is also shown to have an impact on the range of predicted creep life.

Jones, Thomas C.↗
NASA NTRS2010

Maintaining a Local Data Integration System in Support of Weather Forecast Operations

Since 2000, both the National Weather Service in Melbourne, FL (NWS MLB) and the Spaceflight Meteorology Group (SMG) have used a local data integration system (LDIS) as part of their forecast and warning operations. Each has benefited from 3-dimensional analyses that are delivered to forecasters every 15 minutes across the peninsula of Florida. The intent is to generate products that enhance short-range weather forecasts issued in support of NWS MLB and SMG operational requirements within East Central Florida. The current LDIS uses the Advanced Regional Prediction System (ARPS) Data Analysis System (ADAS) package as its core, which integrates a wide variety of national, regional, and local observational data sets. It assimilates all available real-time data within its domain and is run at a finer spatial and temporal resolution than current national- or regional-scale analysis packages. As such, it provides local forecasters with a more comprehensive and complete understanding of evolving fine-scale weather features. Recent efforts have been undertaken to update the LDIS through the formal tasking process of NASA's Applied Meteorology Unit. The goals include upgrading LDIS with the latest version of ADAS, incorporating new sources of observational data, and making adjustments to shell scripts written to govern the system. A series of scripts run a complete modeling system consisting of the preprocessing step, the main model integration, and the post-processing step. The preprocessing step prepares the terrain, surface characteristics data sets, and the objective analysis for model initialization. Data ingested through ADAS include (but are not limited to) Level II Weather Surveillance Radar- 1988 Doppler (WSR-88D) data from six Florida radars, Geostationary Operational Environmental Satellites (GOES) visible and infrared satellite imagery, surface and upper air observations throughout Florida from NOAA's Earth System Research Laboratory/Global Systems Division/Meteorological Assimilation Data Ingest System (MADIS), as well as the Kennedy Space Center ICape Canaveral Air Force Station wind tower network. The scripts provide NWS MLB and SMG with several options for setting a desirable runtime configuration of the LDIS to account for adjustments in grid spacing, domain location, choice of observational data sources, and selection of background model fields, among others. The utility of an improved LDIS will be demonstrated through postanalysis warm and cool season case studies that compare high-resolution model output with and without the ADAS analyses. Operationally, these upgrades will result in more accurate depictions of the current local environment to help with short-range weather forecasting applications, while also offering an improved initialization for local versions of the Weather Research and Forecasting model.

Watson, Leela R.↗
NASA NTRS1991

Three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The case considered was the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge.

Davoudzadeh, Farhad↗
NASA NTRS2011

An Overview of the GEOS-5 Aerosol Reanalysis

GEOS-5 is the latest version of the NASA Global Modeling and Assimilation Office (GMAO) earth system model. GEOS-5 contains components for atmospheric circulation and composition (including data assimilation), ocean circulation and biogeochemistry, and land surface processes. In addition to traditional meteorological parameters, GEOS-5 includes modules representing the atmospheric composition, most notably aerosols and tropospheric/stratospheric chemical constituents, taking explicit account of the impact of these constituents on the radiative processes of the atmosphere. MERRA is a NASA meteorological reanalysis for the satellite era (1979-present) using GEOS-5. This project focuses on historical analyses of the hydrological cycle on a broad range of weather and climate time scales. As a first step towards an integrated Earth System Analysis (IESA), the GMAO is extending MERRA with reanalyses for other components of the earth system: land, ocean, bio-geochemistry and atmospheric constituents. In this talk we will present results from the MERRA-driven aerosol reanalysis covering the Aqua period (2003-present). The assimilation of Aerosol Optical Depth (AOD) in GEOS-5 involves very careful cloud screening and homogenization of the observing system by means of a Neural Net scheme that translates MODIS radiances into AERONET calibrated AOD. These measurements are further quality controlled using an adaptive buddy check scheme, and assimilated using the Local Displacement Ensemble (LDE) methodology. For this reanalysis, GEOS-5 runs at a nominal 50km horizontal resolution with 72 vertical layers (top at approx. 8Skm). GEOS-5 is driven by daily biomass burning emissions derived from MODIS fire radiative power retrievals. We will present a summary of our efforts to validate such dataset. The GEOS-5 assimilated aerosol fields are first validated by comparison to independent in-situ measurements (AERONET and PM2.5 surface concentrations). In order to asses aerosol absorption on a global scale, we perform a detailed radiative transfer calculation to simulate the UV aerosol index, comparing our results to OMI measurements. By simulating aerosol attenuated backscatter, we use CALIPSO measurements to evaluate the vertical structure of our aerosol estimates, in particular in regions where we have larger discrepancies with OMI. Finally, the consistency of our AOD estimates with estimates from MISR, MODIS/Deep Blue, OMI and PARASOL will be briefly discussed.

da Silva, Arlindo↗
NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1998

Creep Strain and Strain Rate Response of 2219 Al Alloy at High Stress Levels

As a result of high localized plastic deformation experienced during proof testing in an International Space Station connecting module, a study was undertaken to determine the deformation response of a 2219-T851 roll forging. After prestraining 2219-T851 Al specimens to simulate strains observed during the proof testing, creep tests were conducted in the temperature range from ambient temperature to 107 C (225 F) at stress levels approaching the ultimate tensile strength of 2219-T851 Al. Strain-time histories and strain rate responses were examined. The strain rate response was extremely high initially, but decayed rapidly, spanning as much as five orders of magnitude during primary creep. Select specimens were subjected to incremental step loading and exhibited initial creep rates of similar magnitude for each load step. Although the creep rates decreased quickly at all loads, the creep rates dropped faster and reached lower strain rate levels for lower applied loads. The initial creep rate and creep rate decay associated with primary creep were similar for specimens with and without prestrain; however, prestraining (strain hardening) the specimens, as in the aforementioned proof test, resulted in significantly longer creep life.

Taminger, Karen M. B.↗
NASA NTRS2021

Seasonal Glacier and Snow Loading in Svalbard Recovered from Geodetic Observations

We processed time series from seven Global Navigation Satellite System (GNSS) stations and one Very Long Baseline Interferometry (VLBI) station in Svalbard. The goal was to capture the seasonal vertical displacements caused by elastic response of variable mass load due to ice and snow accumulation. We found that estimates of the annual signal in different GNSS solutions disagree by more than 3 mm which makes geophysical interpretation of raw GNSS time series problematic. To overcome this problem, we have used an enhanced Common Mode (CM) filtering technique. The time series are differentiated by the time series from remote station BJOS with known mass loading signals removed a priori. Using this technique, we have achieved a substantial reduction of the differences between the GNSS solutions. We have computed mass loading time series from a regional Climatic Mass Balance (CMB) and snow model that provides the amount of water equivalent at a 1 km resolution with a time step of 7 days. We found that the entire vertical loading signal is present in data of two totally independent techniques at a statistically significant level of 95%. This allowed us to conclude that the remaining errors in vertical signal derived from the CMB model are less than 0.2 mm at that significance level. Refining the land water storage loading model with a CMB model resulted in a reduction of the annual amplitude from 2:1 mm to 1:1 mm in the CM filtered time series, while it had only a marginal impact on raw time series. This provides a strong evidence that CM filtering is essential for revealing local periodic signals when a millimetre level of accuracy is required.

H P Kierulf↗
NASA NTRSDate not supplied

Exploring Innovative Methods for Earth Science Communication Through NASA’s Earth Information Center

Environmental challenges stemming from unprecedented changes in our planet have increased the need to communicate our understanding of Earth as a connected system. In June 2023, NASA unveiled the Earth Information Center (EIC), part of NASA’s Earth Action Strategy aimed at amplifying NASA’s Earth science impact by engaging decision-makers beyond the scientific community. Existing in both physical and virtual space, the EIC provides critical information on how the planet is changing and affecting livelihoods across the globe. For over fifty years, NASA has utilized the unique vantage point space offers to monitor Earth in collaboration with Federal partners. Through an expanding fleet of Earth observing satellites and sensors, NASA informs local to global decision making within nine thematic areas: agriculture, biodiversity, disasters, greenhouse gases, health and air quality, sea level rise and coastal impacts, sustainable energy, water resources, and wildfires. Visitors to the inaugural location of the EIC at NASA Headquarters in Washington D.C., can interact with Earth observation data and models through innovative exhibits and storytelling. Designed by an interdisciplinary team, the EIC is designed for multiple modality learning to reach a wide base of end-users. Data driven visualizations, near real-time information, and curated stories highlight the applications of Earth observations to address environmental challenges. Complementary exhibits and immersive storytelling allow visitors to physically step inside environmental data and connect with information on an emotional level. Taken together, the collective EIC provides scientists and non-scientists alike with the ability to see our home planet as NASA sees it, as a system of systems, while delivering easily accessible information to those who need it most.

Earth Information Center↗
NASA NTRS1985

A fast, time-accurate unsteady full potential scheme

The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

Shankar, V.↗
NASA NTRS2010

A Controller-in-the Loop Simulation of Ground-Based Automated Separation Assurance in a NextGen Environment

A controller-in-the-loop simulation was conducted in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center to investigate the functional allocation aspects associated with ground-based automated separation assurance in a far-term NextGen environment. In this concept, ground-based automation handled the detection and resolution of strategic and tactical conflicts and alerted the controller to deferred situations. The controller was responsible for monitoring the automation and managing situations by exception. This was done in conditions both with and without arrival time constraints across two levels of traffic density. Results showed that although workload increased with an increase in traffic density, it was still manageable in most situations. The number of conflicts increased similarly with a related increase in the issuance of resolution clearances. Although over 99% of conflicts were resolved, operational errors did occur but were tied to local sector complexities. Feedback from the participants revealed that they thought they maintained reasonable situation awareness in this environment, felt that operations were highly acceptable at the lower traffic density level but were less so as it increased, and felt overall that the concept as it was introduced here was a positive step forward to accommodating the more complex environment envisioned as part of NextGen.

Homola, J.↗
NASA NTRS1991

A 1 MW, 100 kV, less than 100 kg space based dc-dc power converter

A 1 MW dc-dc power converter has been designed which has an input voltage of 5 kV +/-3 percent, an output voltage of 100 kV +/- 0.25 percent, and a run time of 1000 s at full power. The estimated system mass is 83.8 kg, giving a power density of 11.9 kW/kg. The system exceeded the weight goal of 10 kW/kg through the use of innovative components and system concepts. The system volume is approximately 0.1 cu m, and the overall system efficiency is estimated to be 87 percent. Some of the unique system features include a 50-kHz H-bridge inverter using MOS-controlled thyristors as the switching devices, a resonance transformer to step up the voltage, open-cycle cryogenic hydrogen gas cooling, and a nonrigid, inflatable housing which provides on-demand pressurization of the power converter local environment. This system scales very well to higher output powers. The weight of the 10-MW system with the same input and output voltage requirements and overall system configuration is estimated to be 575.3 kg. This gives a power density of 17.4 kW/kg, significantly higher than the 11.9 kW/kg estimated at 1 MW.

Cooper, J. R.↗
NASA NTRS1990

Two- and three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction (BVI) problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The two-dimensional study considered the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The 2-D BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge. The three-dimensional interaction study considered the case of a vortex at 20 deg incidence to the blade leading edge. Although the qualitative results were similar to that of the two-dimensional interaction, details clearly showed the three-dimensional nature of the interaction process.

Davoudzadeh, F.↗
NASA NTRS2001

Molecular Simulations in Astrobiology

One of the main goals of astrobiology is to understand the origin of cellular life. In the absence of any record of the earliest ancestors of contemporary cells, protocells, the most direct way to test our understanding of their characteristics is to construct laboratory models of protocells. Such efforts, currently underway in the NASA Astrobiology Program, are accompanied by computational studies aimed at explaining self-organization of simple molecules into ordered structures and developing designs of molecules that are capable of performing protocellular functions. Many of these functions, such as importing nutrients, capturing and storing energy, and responding to changes in the environment, are carried out by proteins bound to membranes. We use computer simulations to address the following, questions about these proteins: (1) How do small proteins (peptides) organize themselves into ordered structures at water-membrane interfaces and insert into membranes? (2) How do peptides aggregate to form membrane-spannin(y structures (e.g., channels)? (3) By what mechanisms do such aggregates perform their functions? The simulations are performed using the molecular dynamics (MD) method. In this method, Newton's equations of motion for each atom in the system are solved iteratively. At each time step, the forces exerted on each atom by the remaining atoms are evaluated by dividing them into two parts. Short-range forces are calculated directly in real space while long-range forces are evaluated in reciprocal space, usually using a particle-mesh algorithm which is of order O(NlnN). Currently, a time step of 2 femtoseconds is typically used, thereby making studies of problems occurring on multi-nanosecond time scales (10(exp 6) - 10(exp 8) time steps) accessible. To address a broader range of problems, simulations need to be extended by three orders of magnitude. Such an extension requires both algorithmic improvements and codes scalable to a large number of parallel processors. Work in this direction is in progress. Two specific series of simulations that demonstrate how peptides self-organize and function in membranes are discussed. In one series of simulations, it was shown that nonpolar peptides, disordered in water, translocate to the nonpolar interior of the membrane and, simultaneously, fold into two different helical structures, which remain in equilibrium. Once in the membrane, the peptides can readily change their orientation, especially in response to local electric fields. This structural and orientational flexibility of peptides with changing conditions may have provided a mechanism of transmitting signals between the environment and the interior of the protocell. In another series of simulations, the mechanism by which a simple protein channel efficiently mediates proton transport across membranes was investigated. This process is a key step in cellular bioenergetics. In the channel under study, proton transport is gated by four histidines that occlude the channel pore. The simulations demonstrate that protons move through the gate by a "shuttle" mechanism, wherein one histidine is protonated on the extracellular side and, subsequently, the proton bound on the opposite side is released.

Pohorille, Andrew↗
NASA NTRS2000

Gravity independence of seed-to-seed cycling in Brassica rapa

Growth of higher plants in the microgravity environment of orbital platforms has been problematic. Plants typically developed more slowly in space and often failed at the reproductive phase. Short-duration experiments on the Space Shuttle showed that early stages in the reproductive process could occur normally in microgravity, so we sought a long-duration opportunity to test gravity's role throughout the complete life cycle. During a 122-d opportunity on the Mir space station, full life cycles were completed in microgravity with Brassica rapa L. in a series of three experiments in the Svet greenhouse. Plant material was preserved in space by chemical fixation, freezing, and drying, and then compared to material preserved in the same way during a high-fidelity ground control. At sampling times 13 d after planting, plants on Mir were the same size and had the same number of flower buds as ground control plants. Following hand-pollination of the flowers by the astronaut, siliques formed. In microgravity, siliques ripened basipetally and contained smaller seeds with less than 20% of the cotyledon cells found in the seeds harvested from the ground control. Cytochemical localization of storage reserves in the mature embryos showed that starch was retained in the spaceflight material, whereas protein and lipid were the primary storage reserves in the ground control seeds. While these successful seed-to-seed cycles show that gravity is not absolutely required for any step in the plant life cycle, seed quality in Brassica is compromised by development in microgravity.

Flight Experiment↗
NASA NTRS1995

An Extended Lagrangian Method

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Liou, Meng-Sing↗
NASA NTRS1998

Parallel Directionally Split Solver Based on Reformulation of Pipelined Thomas Algorithm

In this research an efficient parallel algorithm for 3-D directionally split problems is developed. The proposed algorithm is based on a reformulated version of the pipelined Thomas algorithm that starts the backward step computations immediately after the completion of the forward step computations for the first portion of lines This algorithm has data available for other computational tasks while processors are idle from the Thomas algorithm. The proposed 3-D directionally split solver is based on the static scheduling of processors where local and non-local, data-dependent and data-independent computations are scheduled while processors are idle. A theoretical model of parallelization efficiency is used to define optimal parameters of the algorithm, to show an asymptotic parallelization penalty and to obtain an optimal cover of a global domain with subdomains. It is shown by computational experiments and by the theoretical model that the proposed algorithm reduces the parallelization penalty about two times over the basic algorithm for the range of the number of processors (subdomains) considered and the number of grid nodes per subdomain.

Povitsky, A.↗
NASA NTRS2012

Coronal Magnetic Field Measurement Using CME-Driven Shock Observations

Collisionless shocks form ahead of coronal mass ejections (CMEs) when the CME speed exceeds the Alfven speed of the ambient plasma in the corona and interplanetary medium. The shock stands at a distance from the CME flux rope that depends on the shock Mach number, the geometry of the driver, and the adiabatic index. While the shock ahead of the CME has been observed for a long time in the in situ data, it has been identified recently near the Sun in the coronagraphic and EUV images. Unlike in situ observations, the imaging observations are two dimensional, so one can better discern the CME-shock relationship near the Sun. Gopalswamy and Yashiro demonstrated that the coronal magnetic field can be derived from the shock standoff distance measured in coronagraphic images. The method involves measuring the standoff distance, the radius of curvature of the flux rope, and assuming the value of the adiabatic index and deriving the Alfvenic Mach number. The next step is to derive the Alfvenic Mach number from the measured shock speed and an estimate of the local solar wind speed. The final step involves deriving the magnetic field from the Alfven speed by measuring the local plasma density either from coronagraphic (polarized brightness) images or from the band-splitting of type II radio bursts. In this paper, we derive the combined magnetic field profile from near the Sun to the edge of the LASCO field of view (1.5 to 30 solar radii) and compare it with the current model profiles.

Gopalswarmy, Nat↗