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At least 1,711 records · Page 95
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Connecting the Radiative Influences of Aerosol upon the Mass Flux Profiles of Shallow Cumuli across the Southeast Atlantic Ocean Basin and its Boundaries (Final Report)

The Atlantic Ocean covers approximately 25% of Earth’s surface and the atmosphere above it is home to a complex array of clouds and aerosols that have important influences on regional and global weather and climate. These influences must be accurately depicted in short range, medium range, seasonal, and climate forecast models. Conditions over the tropical Atlantic are particularly complex due to continental scale plumes of dust from the Sahara Desert and smoke from agricultural burning in Africa that drift across the Atlantic Ocean basin toward the Americas. These plumes are often found meandering in the lower atmosphere above shallow tropical clouds that form above the ocean surface, presumably mingling with these clouds on occasion due to convective mixing processes. Elevated dust and smoke particles absorb incoming sunlight and substantially warm the marine atmosphere in the layer in which they are present. This warming may alter the thermal stability of the marine atmosphere and may throttle or enhance the development of clouds, change their internal structure and the rate at which they precipitate. Alternatively, it may isolate the lower atmosphere from drier layers above enabling water vapor to accumulate near the ocean surface potentially leading to the development of deeper convection. Our study was organized around the principal concept of determining the impact of African smoke and dust plumes upon cloud development at ASI and understanding how a popular shallow convection parameterization used in models responds to the presence of this aerosol. We analyzed observations collected during the US Department of Energy (DOE) Layered Atlantic Smoke Interactions with Clouds (LASIC) campaign using the Atmospheric Radiation Measurement Program’s Mobile Facility #1 (AMF-1), which was deployed to Ascension Island (ASI) in Southeastern Atlantic for a one-year period. Ascension Island is immediately downwind from an African source of these plumes, but far enough removed to enable the lower atmosphere to have reacted to their presence. A main goal of our study was to compute radiative heating rate profiles over Ascension Island and along the trajectory from the biomass burning regions along coastal Africa to Ascension Island. To compute the radiative heating rate due to aerosols and clouds, we employed observed profiles of temperature, humidity, and clouds from LASIC alongside aerosol optical properties from the Modern-era Retrospective analysis for Research and Applications Version 2 (MERRA-2), as input for the Rapid Radiation Transfer Model (RRTM). Radiative heating was also assessed across the southeast Atlantic Ocean using an ensemble of back trajectories from the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model. We were successful in this effort and the resulting publication is already being cited despite its relatively short lifetime in the literature. The second part of our study involved the process-level representation of the clouds observed over the Southeastern Atlantic in models. Our initial task, upon which the balance of this portion of the study depended, was to evaluate the representativeness of the clouds observed by AMF-1. What orographic influence did Ascension Island have on the measured cloud structure? We set out to answer this question by trying to separate observations that were clearly indicative of orographic forcing from those that were representative of open ocean. The siting of AMF-1, which was 340-m above sea-level on the slope of a steep escarpment, proved demonstrably problematic for cloud process measurements. Despite considerable effort using multiple approaches including artificial intelligence (AI), we were unable to successfully compensate for the orographic forcing present at the AMF-1 site on ASI and, hence, produce process-level summaries of the convective mass flux representative of open ocean over the Southeastern Atlantic. Even though the project has officially ended, we are making a final attempt using two new types of clustering algorithm (i.e., AI) on the recommendation of a former student, who is an expert in this area. Since we have only recently begun to test these new AI schemes, the recommendations from the second part of our project outlined below are based on our experience at the time of this report.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2007

Lunar Return Reentry Thermal Analysis of a Generic Crew Exploration Vehicle Wall Structures

Thermostructural analysis was performed on generic crew exploration vehicle (GCEV) heat shielded wall structures subjected to reentry heating rates based on five potential lunar return reentry trajectories. The GCEV windward outer wall is fabricated with a graphite/epoxy composite honeycomb sandwich panel and the inner wall with an aluminum honeycomb sandwich panel. The outer wall is protected with an ablative Avcoat-5026-39H/CG thermal protection system (TPS). A virtual ablation method (a graphical approximation) developed earlier was further extended, and was used to estimate the ablation periods, ablation heat loads, and the TPS recession layer depths. It was found that up to 83 95 percent of the total reentry heat load was dissipated in the TPS ablation process, leaving a small amount (3-15 percent) of the remaining total reentry heat load to heat the virgin TPS and maintain the TPS surface at the ablation temperature, 1,200 F. The GCEV stagnation point TPS recession layer depths were estimated to be in the range of 0.280-0.910 in, and the allowable minimum stagnation point TPS thicknesses that could maintain the substructural composite sandwich wall at the limit temperature of 300 F were found to be in the range of 0.767-1.538 in. Based on results from the present analyses, the lunar return abort ballistic reentry was found to be quite attractive because it required less TPS weight than the lunar return direct, the lunar return skipping, or the low Earth orbit guided reentry, and only 11.6 percent more TPS weight than the low Earth orbit ballistic reentry that will encounter a considerable weight penalty to obtain the Earth orbit. The analysis also showed that the TPS weight required for the lunar return skipping reentry was much more than the TPS weight necessary for any of the other reentry trajectories considered.

Ko, William L.↗
NASA NTRS1993

A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles

Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined Eulerian-Lagrangian technique, in which Eulerian conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.

Dejong, Frederik J.↗
NASA NTRS1995

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Chuang, C.-H.↗
NASA NTRS1992

Error Analysis of Combined Optical-Flow and Stereo Passive Ranging

The motion of an imaging sensor causes each imaged point of the seem to describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (eg, of liquid) which is the source of the term "optical flow". Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute range to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound (CRLB) is developed for the combined system under the assumption of a random angular misalignment common to both cameras of a stereo pair. It is shown that the range accuracy degradations caused by misalignment is negligible for a combined optical-flow and stereo system as compared with a monocular optical-flow system.

Barniv, Yair↗
NASA NTRS2010

Analysis of Flight Management System Predictions of Idle-Thrust Descents

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the predictor and its uncertainty models, descents from cruise to the meter fix were executed using vertical navigation in a B737-700 simulator and a B777-200 simulator, both with commercial FMSs. For both aircraft types, the FMS computed the intended descent path for a specified speed profile assuming idle thrust after top of descent (TOD), and then it controlled the avionics without human intervention. The test matrix varied aircraft weight, descent speed, and wind conditions. The first analysis in this paper determined the effect of the test matrix parameters on the FMS computation of TOD location, and it compared the results to those for the current ground predictor in the Efficient Descent Advisor (EDA). The second analysis was similar but considered the time to fly a specified distance to the meter fix. The effects of the test matrix variables together with the accuracy requirements for the predictor will determine the allowable error for the predictor inputs. For the B737, the EDA prediction of meter fix crossing time agreed well with the FMS; but its prediction of TOD location probably was not sufficiently accurate to enable idle-thrust descents in congested airspace, even though the FMS and EDA gave similar shapes for TOD location as a function of the test matrix variables. For the B777, the FMS and EDA gave different shapes for the TOD location function, and the EDA prediction of the TOD location is not accurate enough to fully enable the concept. Furthermore, the differences between the FMS and EDA predictions of meter fix crossing time for the B777 indicated that at least one of them was not sufficiently accurate.

Stell, Laurel↗
DOE OSTI2021

A Geometry-Driven Longitudal Topic Model

A simple and scalable framework for longitudinal analysis of Twitter data is developed that combines latent topic models with computational geometric methods. Dimensionality reduction tools from computational geometry are applied to learn the intrinsic manifold on which the latent, temporal topics reside. Then shortest path distances on the manifold are used to link together these topics. The proposed framework permits visualization of the low-dimensional embedding which provides clear interpretation of the complex, high-dimensional trajectories that may exist among latent topics. Practical application of the proposed framework is demonstrated through its ability to capture and effectively visualize natural progression of latent COVID-19 related topics learned from Twitter data. Interpretability of the trajectories is achieved by comparing to real-world events. In addition, the framework permits study of spatial variation in Twitter behavior for learned topics. The analysis demonstrates that the proposed framework is able to capture granular-level impact of COVID-19 on public discussions. We end by arguing that Twitter data, when analyzed within the proposed framework, can serve as a valuable supplementary data stream for COVID-related studies.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Atmospheric Models for Aeroentry and Aeroassist

Eight destinations in the Solar System have sufficient atmosphere for aeroentry, aeroassist, or aerobraking/aerocapture: Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, plus Saturn's moon Titan. Engineering-level atmospheric models for Earth, Mars, Titan, and Neptune have been developed for use in NASA s systems analysis studies of aerocapture applications. Development has begun on a similar atmospheric model for Venus. An important capability of these models is simulation of quasi-random perturbations for Monte Carlo analyses in developing guidance, navigation and control algorithms, and for thermal systems design. Characteristics of these atmospheric models are compared, and example applications for aerocapture are presented. Recent Titan atmospheric model updates are discussed, in anticipation of applications for trajectory and atmospheric reconstruct of Huygens Probe entry at Titan. Recent and planned updates to the Mars atmospheric model, in support of future Mars aerocapture systems analysis studies, are also presented.

Justus, C. G.↗
NASA NTRS2005

Atmospheric Models for Aeroentry and Aeroassist

Eight destinations in the Solar System have sufficient atmosphere for aeroentry, aeroassist, or aerobraking/aerocapture: Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, plus Saturn's moon Titan. Engineering-level atmospheric models for Earth, Mars, Titan, and Neptune have been developed for use in NASA's systems analysis studies of aerocapture applications. Development has begun on a similar atmospheric model for Venus. An important capability of these models is simulation of quasi-random perturbations for Monte Carlo analyses in developing guidance, navigation and control algorithms, and for thermal systems design. Characteristics of these atmospheric models are compared, and example applications for aerocapture are presented. Recent Titan atmospheric model updates are discussed, in anticipation of applications for trajectory and atmospheric reconstruct of Huygens Probe entry at Titan. Recent and planned updates to the Mars atmospheric model, in support of future Mars aerocapture systems analysis studies, are also presented.

Justus, C. G.↗
NASA NTRS2024

Flight Mechanics Modeling and Simulation of the Earth Entry System

Introduction: The Mars Sample Return (MSR) Campaign being planned by NASA and ESA has the ambitious goal to return Mars samples back to Earth. This international collaboration had developed a concept of operations that included a ESA-designed Earth Return Orbiter (ERO) and NASA-designed Capture, Containment, and Return System (CCRS). The Earth Entry System (EES), consisting of a protective aeroshell that houses the samples as well as sample containment vessels, would conduct entry, descent, and landing (EDL) on a direct Earth trajectory. The EES would enter on a spin-stabilized ballistic trajectory with the goal to passively achieve aerodynamic stability throughout all regions of flight. The EDL sequence would end with the EES impacting the soft playa soil of the Utah Test and Training Range (UTTR). As of the submission of this abstract, the MSR campaign is undergoing a re-architecture leading to a pause in EES development. However, the novel approaches developed in flight mechanics modeling and simulation can significantly benefit the greater IPPW community in the development of Earth return vehicles. This paper will present the latest state of EES flight mechanics modeling and simulation. The paper will highlight the simulation architecture developed and key lessons learned from understanding of EDL trajectory sensitivities. Modeling and Simulation: Figure 1 provides a high-level concept of operations for the approach, entry, descent, and landing (AEDL) phase of the CCRS-portion of MSR. The objective of EES flight mechanics is to model and simulate the EES trajectory from ERO separation to ground impact at UTTR. A variety of flight mechanics simulation models were utilized to model both exo-atmopsheric and atmospheric portions of flight. 42, a 6-DOF simulation developed at Goddard Space Flight Center, is utilized for propagating the attitude of EES during exo-atmospheric flight. 42 allows for a variety of spin eject mechanism scenarios to be simulated for analysis. 10 minutes prior to entry, the 42 states are handed off to the EDL sims. The prime EDL sim utilized by EES is the Program to Optimize Simulated Trajectories II (POST2), a 6-DOF sim developed at Langley Research Center, and the independent verification and validation EDL sim utilized is DSENDS, a 6-DOF sim developed at Jet Propulsion Laboratory. Figure 2 provides a visualization of the flight mechanics simulation model flow through various points in the AEDL phase. Due to the existence of a variety of sim models, the EES flight mechanics team developed processes for data hand-off. These processes included the development of a centralized coordinate frame document, utilization of a single, centralized simulation input document for all sims to reference, and hand-off files containing both the technical data to be ingested by other flight mechanics sims as well as annotations of modeling assumptions utilized to generate the data. Figure~\ref{fig:post2simarchitecture} provides an overview of the POST2 sim architecture wherein POST2 ingests numerous subsystem models and input files. The dispersed state file generated by MONTE provides the position/velocity state of the trajectory while the 42 Handoff file provides the attitude. The aerodynamics database, delivered by the EES aeroscience team, is utilized to simulate the aerodynamic forces and moments experienced during EDL. A custom atmosphere model, developed by EES atmosphere team, is utilized to simulate the anticipated atmosphere environment around the region of Earth through which the EES trajectory flys. These inputs and subsystem models can be varied depending on the AEDL flight mechanics scenario being simulated. Monte Carlo simulations are utilized to generate statistical AEDL performance metrics in the form of scorecards and violin plots. Furthermore, outputs from the POST2 simulation are utilized for follow-on analyses including aerothermal and landing performance. \section{Flight Mechanics Lessons Learned} Though the EES flight mechanics team uncovered a variety of lessons learned through the analysis conducted to support CCRS through preliminary design review, this paper will highlight the most important lessons. A key AEDL performance goal is to ensure the landing footprint of EES remains on the UTTR south range. A common modeling strategy used in EDL analysis is One-Variable-At-a-Time (OVAT). OVAT analysis provides insight into the key drivers that affect AEDL performance metrics. Figure 3 shows the landing ellipses for single dispersion sources as compared to the baseline aggregate of all dispersions. The figure shows that atmosphere winds alone dominate the size of the footprint ellipse (note: EES does not use a parachute unlike previous Earth-return missions and is in wind-driven free fall for ~5min). The significance of the wind led the EES flight mechanics team to pursue the development of a Custom Atmosphere Model [4], in lieu of EarthGRAM [1], built on actual radiosonde wind measurements around the UTTR-region. This decision was driven by the realism in the generated footprint ellipses and lessons-learned from Stardust [5]. These findings will be invaluable for future Earth-return missions in providing an early understanding of the key drivers affecting footprint size and modeling considerations for which to account. Another lesson learned is tied to the AEDL performance goal of achieving passive stability throughout all regions of flight. It is well understood that blunt-body aeroshells are less stable as they transition from supersonic to subsonic. Eliminating a backshell does help improvestability; however, other phenomena such as roll-induced instability during terminal descent can still arise. The EES flight mechanics team developed stability metrics as tools to better understand the causes of and better predict the onset of dynamic instability. These tools were built upon analytical models developed by Jaffe [3] and Murphy [2]. The tools were shown to both be very accurate in correlation with actual unstable cases and useful in developing stability margin policies based on the vehicle design and simulation considerations (e.g. sphere-cone angle change, mass change, wind turbulence). These tools allowed for the current EES design to demonstrate the ability to achieve passive stability and can be an invaluable tool for consideration in the design of parachute-less Earth-return vehicles.

Rohan Deshmukh↗
DOE OSTI2025

One Million Open-source Cislunar Orbits

Cislunar space, encompassing the region from geosynchronous orbit to beyond the Moon, is poised to become a cornerstone for future exploration, scientific discovery, and national security. Missions in this region, spanning durations from weeks to decades, require robust infrastructure and reliable transit capabilities. The complex gravitational influences of the Moon, Sun, and planets, along with thermal radiation from Earth and the Sun, lead to significant trajectory deviations, resulting in kilometer-scale errors within days. Leveraging the high-performance computing resources at Lawrence Livermore National Laboratory (LLNL), we have simulated one million high-fidelity cislunar trajectories, now publicly available via LLNL’s Green Data Oasis and the Unified Data Library. Generated using the open-source Space Situational Awareness Python package, these trajectories match the precision of commercial tools such as AGI’s Systems Tool Kit and NASA’s General Mission Analysis Tool. This data set is a valuable resource for reference, statistical analysis of cislunar orbit populations, and training machine learning models for rapid orbit classification with minimal observational input. Preliminary analysis reveals stable bands in Keplerian element space, particularly around five geosynchronous radii across a range of inclinations and eccentricities. Beyond this threshold, the Moon’s influence disrupts most unassisted orbits, though co-orbiting L4/L5 Lunar Trojans persist throughout the six-year simulation.

Astronomy and AstroPhysics↗
NASA NTRS1973

Results on the energy dependence of cosmic-ray charge composition

Results of measurements by a balloon-borne ionization spectrometer of the energy dependence of high-energy cosmic-ray charge composition. The results presented are greatly improved over those obtained earlier by Ormes et al. (1971) by the use of a multidimensional charge analysis with more efficient background rejection, and a more accurate energy determination. Complex couplings between the charge, energy, and trajectory information were taken into account and are discussed. The spectra of individual elements up to oxygen and of groups of nuclei up through iron were measured up to almost 100 GeV per nucleon. The energy spectrum of the secondary nuclei, B + N, is found to be steeper than that of the primary nuclei, C + O, in agreement with Smith et al. (1973). The most dramatic finding is that the spectrum of the iron nuclei is flatter than that of the carbon and oxygen nuclei by 0.57 plus or minus 0.14 of a power.

Balasubrahmanyan, V. K.↗
NASA NTRS1977

Lunar far side sample return missions using the Soviet Luna system

The paper assesses the feasibility of using the Soviet Lunar Sample Return vehicle in cooperation with the United States to return a sample of lunar soil from the far side of the moon. Analysis of the orbital mechanics of the Luna system shows how landing sites are restricted on the moon. The trajectory model is used to duplicate the 3 Luna missions flown to date and the results compared to actual Soviet data. The existence of suitable trajectories for the earth return trip is assessed, including landing dispersions at earth. Several possible areas of technical difficulty are identified.

Roberts, P. H., Jr.↗
NASA NTRS1982

Preliminary analysis of STS-2 entry flight data

A preliminary analysis of the data obtained during the entry of the STS-2 flight was completed. The stability and control derivatives from STS-2 were examined. Questions still remain throughout the flight envelope and the area below Mach 3 needs more study. With three controls operating in a high gain feedback system, it is difficult to separate the individual effects of each of the controls. Analysis of the aerothermal data shows that wing structural-temperature measurements are generally repeatable and consistent with the trajectories. The measured wing upper surface temperatures are in reasonable agreement with Dryden predictions but wing lower surface temperatures are higher than Dryden predictions. Heating and heat transfer models will be adjusted to improve the temperature prediction capability for future trajectories.

Source record↗
NASA NTRS1982

Ageostrophic winds and vertical motion fields accompanying upper level jet streak propagation during the Red River Valley tornado outbreak

Preliminary results are shown relating the ageostrophic wind field, through the terms of a semigeostrophic wind equation (assuming adiabatic conditions and the geostrophic momentum approximation) to both air parcel trajectories and their vertical motion fields computed from the parcels' displacement on isentropic surfaces, with respect to pressure. The analysis of results considers both upper-level (324 K) ageostrophic fields and low-level (304 K) fields. Preliminary results tend to support Uccellini and Johnson's (1979) hypothesis concerning upper-level-jet/low-level-jet (ULJ/LLJ) coupling in the exit region of the ULJ. Future plans are described briefly for research intended to clarify the mechanism behind ULJ streak propagation, LLJ development and their relationship to the initiation of severe convection.

Moore, J. T.↗
NASA NTRS1983

Space shuttle orbiter reaction control subsystem flight data anomalies

Shuttle orbiter vehicle flight data obtained during operation of the reaction control subsystem (RCS) were compared with predictions derived from RCS wind tunnel test data. This paper reviews the derivation of the wind tunnel data base and discusses how it was used to predict the full-scale RCS effects. Flight and predicted data comparisons include the lateral and directional aerodynamic effects of firing the side jets, longitudinal aerodynamics for pitch jets, and lateral aerodynamics for roll jets. Flight data anomalies resulting from wind tunnel limitations in representing portions of the entry flight trajectory are presented. The cause of each data anomaly is described, as well as a requirement for additional technical analysis to establish RCS effect simulation parameters that can be used to update jet effect technology.

Stone, J. S.↗
NASA NTRS1985

Monte Carlo calculations of relativistic solar proton propagation in interplanetary space

Particle fluxes and pitch angle distributions of relativistic solar protons at 1 AU were determined by Monte Carlo calculations. The analysis covers two hours after the release of the particles from the Sun and total of eight 100000 particle trajectories were simulated. The pitch angle scattering was assumed to be isotropic ad the scattering mean free path was varied from 0.1 to 4 AU. As an application, the solar injection time and interplanetary scattering mean free path of particles that gave rise to the GLE on May, 1978 were determined. Assuming exponential form, the injection decay time was found to be about 11 minutes. The m.f.p. of pitch angle scattering during the event was about 1 AU.

Lumme, M.↗
NASA NTRS1988

The possible role of meridional flows in suppressing magnetic buoyancy

The equation of motion for a toroidal flux ring in a stellar convective envelope is derived, and the equilibrium of such a ring is considered. Necessary conditions for the stability of toroidal flux rings are derived, and results of stability calculations for a particular model of the meridional flow are presented. The motions of the flux rings when the rings are far from their equilibrium position or when equilibrium does not exist are considered. The results confirm the linear stability analysis, and show that in the absence of stable equilibrium, the rings move toward the solar surface along a trajectory which is parallel to the rotation axis. It is expected that viscosity will tend to reduce the rotational velocity difference between the flux ring and its surroundings, thus reducing the Coriolis force and altering the equilibrium. The storage time of toroidal flux rings is estimated, and some implications for the sun are discussed.

Van Ballegooijen, A. A.↗