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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Proton distribution visualization in perovskite nickelate devices utilizing nanofocused x rays

We use a 30-nm x-ray beam to study the spatially resolved properties of a SmNiO 3 -based nanodevice that is doped with protons. The x-ray absorption spectra supported by density-functional theory simulations show partial reduction of nickel valence in the region with high proton concentration, which leads to the insulating behavior. Concurrently, x-ray diffraction reveals only a small lattice distortion in the doped regions. Together, our results directly show that the knob which proton doping modifies is the electronic valency and not the crystal lattice. Overall, the studies are relevant to ongoing efforts to disentangle structural and electronic effects across metal-insulator phase transitions in correlated oxides.

36 MATERIALS SCIENCE↗
NASA NTRS1986

Time dependent wind fields

Two tasks were performed: (1) determination of the accuracy of Seasat scatterometer, altimeter, and scanning multichannel microwave radiometer measurements of wind speed; and (2) application of Seasat altimeter measurements of sea level to study the spatial and temporal variability of geostrophic flow in the Antarctic Circumpolar Current. The results of the first task have identified systematic errors in wind speeds estimated by all three satellite sensors. However, in all cases the errors are correctable and corrected wind speeds agree between the three sensors to better than 1 ms sup -1 in 96-day 2 deg. latitude by 6 deg. longitude averages. The second task has resulted in development of a new technique for using altimeter sea level measurements to study the temporal variability of large scale sea level variations. Application of the technique to the Antarctic Circumpolar Current yielded new information about the ocean circulation in this region of the ocean that is poorly sampled by conventional ship-based measurements.

Chelton, D. B.↗
NASA NTRS1989

The SMM UV observations of Active Region 5395

The Ultraviolet Spectrometer and Polarimeter (UVSP) on the Solar Maximum Mission (SMM) spacecraft was used extensively to study the spatial morphology and time variability of solar active regions in the far UV (at approx. wavelength of 1370 A) since July 1985. The normal spatial resolution of UVSP observations in this 2nd-order mode is 10 sec., and the highest temporal resolution is 64 milliseconds. To make a full-field, 4 min. by 4 min. image this wavelength using 5 sec. raster steps takes about 3 minutes. UVSP can also make observations of the Sun at approx. wavelength of 2790 with 3 sec. spatial resolution when operated in its 1st-order mode; a full-field image at this wavelength (a so-called SNEW image) takes about 8 minutes. UVSP made thousands of observations (mostly in 2nd-order) of AR 5395 during its transit across the visible solar hemisphere (from 7 to 19 March, inclusive). During this period, UVSP's duty cycle for observing AR 5395 was roughly 40 percent, with the remaining 60 percent of the time being fairly evenly divided between aeronomy studies of the Earth's atmosphere and dead time due to Earth occultation of the Sun. UVSP observed many of the flares tagged to AR 5395, including 26 GOES M-level flares and 3 X-level flares, one of which produced so much UV emission that the safety software of UVSP turned off the detector to avoid damage due to saturation. Images and light curves of some of the more spectacular of the AR 5395 events are presented.

Drake, Stephen A.↗
NASA NTRS2018

Assessing Alternatives in the Systems Engineering Process: Case Study of an Earth Observing Satellite Concept

Defining design alternatives constitutes one of the critical initial steps of the systems engineering process. Once these design alternatives have been identified, assessing which alternatives best satisfy the project’s objectives can prove to be challenging when dealing with complex decision frameworks. Complex systems often involve the participation of different interest groups, who have different value systems and are focused on distinct aspects of the project. For example, design alternatives might be assessed predominantly for their technical merit by one group of stakeholders, while a different group might be more inclined to assess the design alternatives primarily based on programmatic values. MESCAL (Monitoring the Evolving State of Clouds and Aerosol Layers) is an ongoing NASA / CNES (Centre National d’Etudes Spatiales) joint study for an active remote sensing Earth observing satellite. Several design alternatives have been identified and the assessment of these alternatives requires consideration of a variety of factors. This paper presents the approach that was used to support a global assessment of the MESCAL design alternatives. A mapping of the interactions between mission, instrument, and science requirements was modeled to support the assessment of the trade space. In addition, a set of metrics was developed to structure the assessment that was conducted. Finally, this paper also discusses the general applicability of these metrics to other science mission concepts in the formulation phase.

Ivanco, Marie L.↗
DOE OSTI2021

How much information on precipitation is contained in satellite infrared imagery?

Satellite infrared (IR) brightness temperature providing information on the characteristics of cloud tops is one of the primary input data used for estimating precipitation from satellites. Thus, the natural questions to ask are: Does IR imagery contain more information about precipitation in some regions more than others? What are the factors that lead to such differences? Should we expect the amount of information provided by IR imagery to change with respect to temporal or spatial aggregation? Comprehensive analysis of the accuracy of satellite-based precipitation estimates obtained from any given algorithm may provide qualitative answers to the above questions. However, such an approach only offers conclusions within the limited context of the algorithm used to obtain precipitation estimates; that is, patterns caused by the inherent information content of IR imagery are inextricable from those induced by assumptions embedded in the precipitation estimation algorithm. Here, we address the abovementioned questions from a different perspective using an information-theoretic measure, free of structural assumptions and general to a wide range of relationships, to characterize the average and seasonal dependence between IR imagery provided by satellite sensors in the spectral range (10.7–11.5 μm) and precipitation rates in the contiguous United States (CONUS) across distinct temporal and spatial scales. We analyze a total of more than 1.3 billion pairs of IR and precipitation observations over CONUS, and we observe interesting patterns. First, we show that there is a strong inverse relationship (ρ = - 0.73) between the information content of IR data and the number of no-rain observations; however, its robustness varies regionally and seasonally with less significant correlation during the warm season. Second, we demonstrate that the intuitive relationship of increasing dependence between IR and precipitation as a result of temporal or spatial aggregation exhibits a diminishing returns behavior. For instance, temporal aggregation from 1 to 3 h increases the dependence approximately 7 times as much as temporal aggregation from 12 to 24 h. Furthermore, we quantitatively examine and re-confirm several statements previously reported in the literature such as the strong association between IR and precipitation in convective storms and the low association in orographic rainfall. Finally, we conclude by illustrating the potential of the analysis in diagnosis of operational algorithms for estimating precipitation from IR brightness temperature. The findings of this study pinpoint spatial domains and time scales at which IR is not an adequate proxy for estimating precipitation. Thus, they can potentially guide the development of operational algorithms that utilize satellite Infrared imagery for estimating, downscaling and data fusion of precipitation. Finally, the analysis presented here opens up the possibility of developing new methodologies for diagnosis of satellite-based precipitation estimation algorithms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Spatially resolved mass–metallicity relation at $z$ ~ 0.26 from the MUSE-Wide Survey

Galaxies in the local universe have a spatially resolved star-forming main sequence (rSFMS) and mass–metallicity relation (rMZR). We know that the global mass–metallicity relation (MZR) results from the integral of the rMZR, and it evolves with redshift. However, the evolution of the rMZR with redshift is still unclear because the spatial resolution and signal-to-noise ratio are low. Currently, too few observations beyond the local universe are available, and only simulations can reproduce the evolution of the rMZR with redshift. We selected ten emission-line galaxies with an average redshift of $z$ ~ 0.26 from the MUSE-Wide DR1. We obtained the spatially resolved star formation rate (SFR) and metallicity from integral field spectroscopy (IFS), as well as the stellar mass surface density from 3D-HST photometry. We derived the rSFMS and rMZR at $z$ ~ 0.26 and compared them with those of local galaxies. We find that the rSFMS of galaxies at $z$ ~ 0.26 has a slope of ~0.771. The rMZR exists at z ~ 0.26, showing a similar shape to that of the local universe, but a lower average metallicity that is about ~0.11 dex lower than the local metallicity. In addition, we also study the spatially resolved fundamental metallicity relation (rFMR) of these galaxies. However, there is no obvious evidence that an rFMR exists at $z$ ~ 0.26, and it is not an extension of rMZR at a high SFR. Similar to their global versions, the rSFMS and rMZR of galaxies also evolve with redshift. At fixed stellar mass, galaxies at higher redshift show a higher SFR and lower metallicity. In conclusion, these suggest that the evolution of the global galaxy properties with redshift may result from integrating the evolution of the spatially resolved galaxy properties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The High-resolution Urban Meteorology for Impacts Dataset (HUMID) daily for the Conterminous United States

Many current gridded surface meteorological datasets are inadequate for quantifying near surface spatiotemporal variability because they do not fully represent the impacts of land surface heterogeneity. Of note, explicit representation of the spatial structure and magnitude of local urban warming are usually lacking. Here we enhance the representation of spatial meteorological variability over urban areas in the conterminous United States (CONUS) by employing the High-Resolution Land Data Assimilation System (HRLDAS), which accounts for the fine-scale impacts of spatiotemporally varying land surfaces on weather. We also synthesize in situ meteorological data including local mesonets to create a 1 km grid spacing model-observation fusion product spanning 1981-2018 over the CONUS. Daily maximum, minimum, and mean values for a variety of temperature estimates, humidity, and surface energy budget terms, among others, are included. This High-resolution Urban Meteorology for Impacts Dataset (HUMID) will be useful for studies examining spatial variability of near surface meteorology and the impacts of urban heat islands across many disciplines including epidemiology, ecology, and climatology.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1992

Angular relation of axes in perceptual space

The geometry of perceptual space needs to be known to model spatial orientation constancy or to create virtual environments. To examine one main aspect of this geometry, the angular relation between the three spatial axes was measured. Experiments were performed consisting of a perceptual task in which subjects were asked to set independently their apparent vertical and horizontal plane. The visual background provided no other stimuli to serve as optical direction cues. The task was performed in a number of different body tilt positions with pitches and rolls varied in steps of 30 degs. The results clearly show the distortion of orthogonality of the perceptual space for nonupright body positions. Large interindividual differences were found. Deviations from orthogonality up to 25 deg were detected in the pitch as well as in the roll direction. Implications of this nonorthogonality on further studies of spatial perception and on the construction of virtual environments for human interaction is also discussed.

Bucher, Urs↗
DOE OSTI2022

Combining Spatial and Temporal Resolution in Cryo-TEM of Device Materials: Preprint

Cryogenic transmission electron microscopy (cryo-TEM) has been instrumental to reducing the effects of electron-beam sample interactions and enabling higher spatial resolution studies of beam sensitive materials. However, the process of thinning and freezing samples for cryo-TEM characterization is often complex and frequently involves removing materials from their environment or stimuli of interest for extended times. This can allow for structural relaxation, diffusion, and other dynamic processes to occur prior to characterization; for energy materials like battery electrodes, this makes it difficult to precisely correlate the imaged structure with native structures that evolve in-situ during device processing, operation, or aging. Here, we present methods to prepare cryo-TEM samples from energy materials during these critical processes in the relevant device lifetimes. This offers insights into improving the temporal resolution of cryo-TEM, while still exploiting its ability to achieve high spatial resolutions in characterizing beam sensitive materials.

BASIC BIOLOGICAL SCIENCES,MATERIALS SCIENCE↗
NASA NTRS1990

Filtering analysis of a direct numerical simulation of the turbulent Rayleigh-Benard problem

A filtering analysis of a turbulent flow was developed which provides details of the path of the kinetic energy of the flow from its creation via thermal production to its dissipation. A low-pass spatial filter is used to split the velocity and the temperature field into a filtered component (composed mainly of scales larger than a specific size, nominally the filter width) and a fluctuation component (scales smaller than a specific size). Variables derived from these fields can fall into one of the above two ranges or be composed of a mixture of scales dominated by scales near the specific size. The filter is used to split the kinetic energy equation into three equations corresponding to the three scale ranges described above. The data from a direct simulation of the Rayleigh-Benard problem for conditions where the flow is turbulent are used to calculate the individual terms in the three kinetic energy equations. This is done for a range of filter widths. These results are used to study the spatial location and the scale range of the thermal energy production, the cascading of kinetic energy, the diffusion of kinetic energy, and the energy dissipation. These results are used to evaluate two subgrid models typically used in large-eddy simulations of turbulence. Subgrid models attempt to model the energy below the filter width that is removed by a low-pass filter.

Eidson, T. M.↗
DOE OSTI2025

Energy-resolved neutron imaging and diffraction including grain orientation mapping using event camera technology

Time-of-flight neutron diffraction and energy-resolved imaging each provide unique perspectives into material properties. Neutron diffraction is useful for assessing microstructural parameters such as phase composition, texture, and dislocation densities, though it typically provides averaged data over the sampled volume. Energy-resolved imaging, on the other hand, offers both spatial and spectral information by detecting Bragg edges and neutron absorption resonances, which enables detailed mapping of microstructure and isotopic composition. When combined, these techniques have the potential to enrich our understanding of material behavior across different scales, enhancing our understanding of complex materials. Traditionally, these modalities are conducted on separate instruments, which is time-consuming and poses challenges for data integration. Here, we report the integration of the LumaCam, an event-mode energy-resolved neutron imaging camera with the HIPPO time-of-flight diffractometer at LANSCE. This integration enables simultaneous diffraction and imaging across the full spectrum, with analysis optimized for diffraction and Bragg-edge imaging in the thermal range (0.45–10 Å) and resonance imaging in the epithermal range (0.5–3000 eV), facilitating comprehensive multi-modal analysis. We demonstrate its capabilities through case studies, including spatial mapping of grain orientations in a steel sample and accurate thickness estimations for irregular samples including a depleted uranium cylinder and a natural silver-containing mineral specimen. The combined setup enhances real-time sample alignment and provides comprehensive data for crystal structure, texture, and isotopic composition analysis. This approach opens new possibilities for advanced applications in nuclear engineering, archaeology, and materials science.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spatiotemporal Changes in Trace Metal Bioavailability in the Sediment Pore water of a Constructed Wetland Using Passive Pore water Samplers

Sediments in aquatic systems often act as a major sink for contaminants. Diffusive gradient in thin films (DGTs) and in situ equilibrium dialysis samplers (peepers) are two major in situ pore water sampling devices that overcome the problems associated with conventional pore water sampling methods. In the present study, DGTs and peepers were used to study the spatial and seasonal effects (cool months, October–February; warm months, May–September) on metal bioavailability in the H‐02 constructed wetland and the sink versus source role of the sediments by calculating the metal resupply capacity. Data showed similar seasonal trends in metal concentrations using passive samplers, peepers, and DGTs. Pooled Cu and Zn concentrations measured using DGTs were lower in warm months (1.67 ± 1.50 and 2.62 ± 0.68 μg L –1 , respectively, p < 0.001) versus in cool months (2.12 ± 0.65 and 5.58 ± 1.33 μg L –1 , respectively, p < 0.001; mean ± 95% confidence interval). Sulfate (SO 4 2− ) concentrations were significantly (p = 0.0139) lower in warm months (averaged at 0.22 ± 0.05 mg L –1 ) compared to in cool months (0.16 ± 0.05 mg L –1 ). The increase in SO 4 2− concentration is an indicator of the lower activity of sulfate‐reducing bacteria, which need SO 4 2− during anaerobic respiration, in which SO 4 2− is reduced to sulfide (S 2– ) that forms insoluble salts with Cu and Zn, which could partially explain the higher bioavailability of these metals in the cool season. Metal resupply capacity of the sediments was mostly <0.2 for Cu and Zn. Taken together, the H0‐2 wetland sediments mostly acted as a sink to both Cu and Zn over the course of the present study. Environ Toxicol Chem 2023;42:2726–2736. © 2023 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2010

A Mesoscale Analysis of Column-Integrated Aerosol Properties in Northern India During the TIGERZ 2008 Pre-Monsoon Period and a Comparison to MODIS Retrievals

The Indo-Gangetic Plain (IGP) of the northern Indian subcontinent produces anthropogenic pollution from urban, industrial and rural combustion sources nearly continuously and is affected by convection-induced winds driving desert and alluvial dust into the atmosphere during the premonsoon period. Within the IGP, the NASA Aerosol Robotic Network (AERONET) project initiated the TIGERZ measurement campaign in May 2008 with an intensive operational period from May 1 to June 23, 2008. Mesoscale spatial variability of aerosol optical depth (AOD, tau) measurements at 500mn was assessed at sites around Kanpur, India, with averages ranging from 0.31 to 0.89 for spatial variability study (SVS) deployments. Sites located downwind from the city of Kanpur indicated slightly higher average aerosol optical depth (delta Tau(sub 500)=0.03-0.09). In addition, SVS AOD area-averages were compared to the long-tenn Kanpur AERONET site data: Four SVS area-averages were within +/- 1 cr of the climatological mean of the Kanpur site, while one SVS was within 2sigma below climatology. For a SVS case using AERONET inversions, the 440-870mn Angstrom exponent of approximately 0.38, the 440-870mn absorption Angstrom exponent (AAE) of 1.15-1.53, and the sphericity parameter near zero suggested the occurrence of large, strongly absorbing, non-spherical aerosols over Kanpur (e.g., mixed black carbon and dust) as well as stronger absorption downwind of Kanpur. Furthermore, the 3km and lOkm Terra and Aqua MODIS C005 aerosol retrieval algorithms at tau(sub 550) were compared to the TIGERZ data set. Although MODIS retrievals at higher quality levels were comparable to the MODIS retrieval uncertainty, the total number of MODIS matchups (N) were reduced with subsequent quality levels (N=25, QA>=0; N=9,QA>=l; N=6, QA>=2; N=1, QA=3) over Kanpur during the premonsoon primarily due to the semi-bright surface, complex aerosol mixture and cloud-contaminated pixels. The TIGERZ 2008 data set provided a unique opportunity to measure the spatial and temporal variations of aerosol loading in the IGP. The strong aerosol absorption derived from ground-based sun/sky radiometer measurements suggested the presence of a predominately black carbon and dust mixture during the pre-monsoon period. Consistent with the elevated heat-pump hypothesis, these absorbing aerosols found across Kanpur and the greater IGP region during the pre-monsoon period likely induced regional atmospheric warming, which lead to a more rapid advance of the southwest Asian monsoon and above normal precipitation over northern India in June 2008.

Giles, D. M.↗
DOE OSTI2022

Temporal Study 2021-2022: Sensor-Based Time Series of Surface Water Temperature, Specific Conductance, Total Dissolved Solids, Turbidity, pH, and Dissolved Oxygen from across Multiple Watersheds in the Yakima River Basin in Washington, USA (v2)

This dataset supports a broader study examining the drivers of temporal variability in sediment respiration rates in the Yakima River Basin. The dataset provides periodic (weekly or biweekly) in situ hydrological and water chemistry sensor data, handheld sensor water chemistry data, general environmental context photos, and field metadata collected at six sites within multiple rivers in the Yakima River Basin in Washington, USA. In addition to the sensor data, there are plots of continuous in situ sensor data and R scripts used to generate the plots. Related sample-based water chemistry data are published separately at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/1898912.The data package was originally published in September 2022. It was updated in June 2025 (v2; modified files). See the change history section in the readme for more details. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. This dataset is comprised of one main data folder containing two sensor-specific subfolders, and one photographs folder. The main data folder includes file-level metadata (flmd), data dictionary (dd), installation methods, field metadata, handheld sensor data, field data collection protocols, international generic sample number (IGSN) mapping file, and a readme file. Each sensor subfolder (BarotrollAtm and MantaRiverData) contains a subfolder containing sensor timeseries data and plots. The BarotrollAtm Data subfolder contains In Situ Rugged BaroTROLL sensor pressure and air temperature data. The MantaRiverData subfolder contains Eureka Manta+ 35B multisonde temperature, specific conductance, and turbidity. The FieldPhotos folder contains environmental context photographs and videos. All files are .csv, .pdf, .R, .jpg, .jpeg, .heic, .mov, or .mp4.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Linking habitat suitability with a longleaf pine-hardwood model: Building a species-predictive fire-land management framework

Active management of fire-dependent ecosystems for specific species leads to complex tradeoffs, which affect conservation outcomes to other species. Therefore a multi-species evaluation of management actions is required. Habitat Suitability Models (HSMs) can help in predicting the likelihood of species occurrence using corresponding environmental variables and empirical relationships that link occurrence with specific environmental conditions. Incorporating multiple species into HSMs and relating them to habitat dynamics is crucial for ecosystems that require active management with prescribed fire. To address this issue, we developed multi-species HSM driven within an existing population model of the longleaf pine-hardwood ecosystem to assess the suitability of an ecosystem given different fire management strategies and environmental conditions. The population model used in this study provides spatial and temporal changes of longleaf pine-hardwood habitat structure in response to fire. These habitat values are used by the HSM to calculate habitat suitability for three threatened and endangered faunal species of this ecosystem, which all thrive with frequent fire, but have unique habitat requirements. Transient habitat conditions are traced to predict longleaf pine ecosystem trajectories under various management strategies, thereby evaluating current land management actions, such as thinning or prescribed fire frequencies. We tested a suite of environmental conditions to emphasize the sensitivity of the species to different fire management actions. The results of our modeling suggest that maximum suitable habitat for all three species can be achieved with fire frequency occurring at approximately once every three years. The modeling results support current management actions and provide a new habitat assessment tool that incorporates ecological factors for multiple species, thus providing for habitat optimization.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Inhomogeneous distribution of lithium and electrolyte in aged Li-ion cylindrical cells

Carbonate-based electrolytes in Li-ion batteries exhibit long range order in a frozen state, which enables their non-destructive analysis by diffraction methods. In the current study the spatial distribution of lithium and electrolyte inside the graphite anode was determined in cycled Li-ion cells using monochromatic spatially-resolved neutron diffraction measurements at 150 K. The results indicate a loss of lithium and electrolyte and their non-uniform distribution in the graphite anode in aged Li-ion cells. The observed lithium and electrolyte losses are directly correlated with two electrochemical performance degradation mechanisms, which are responsible for the cell capacity fade.

18650-type↗
DOE OSTI2025

Comprehensive techno-economic and life cycle greenhouse gases analysis of green ammonia production utilizing PV and wind energy: Jordan as a case study

Ammonia (NH 3 ) has emerged as a critical player in the global energy transition due to its potential as a low-carbon fuel. Conventional ammonia production methods, primarily through steam methane reforming, are significant contributors to global CO 2 emissions. This study investigates the potential of green ammonia production in Jordan by leveraging the country's abundant solar photovoltaic and wind energy resources. A comprehensive techno-economic and life cycle greenhouse gas analysis was conducted to compare green ammonia production with conventional grey and blue ammonia pathways. Here, the study utilized spatial mapping to assess renewable energy capacity factors across Jordan and optimized the integration of hybrid PV/wind systems with proton exchange membrane (PEM) electrolyzers. The results indicate that the levelized cost of green ammonia (LCOA) in Jordan varies between 900 USD/kg NH 3 and 2500 USD/kg NH 3 which is significantly higher than grey ammonia (similar to 360 USD/kg NH 3 ). Nevertheless, the carbon intensity of green ammonia production (between 0.1 kg CO 2eq /kg NH 3 and 0.5 kg CO 2eq /kg NH 3 ) is much lower than the grey ammonia (1.8 kg CO 2eq /kg NH 3 ). Finally, the results indicate that considering future reductions in capital costs and advancement in renewable energy systems and PEM electrolyzers as well as the ability to sell the co-product O 2 can reduce the LCOA by up to 92 % and make it competitive with grey ammonia.

Green Ammonia↗
DOE OSTI2021

Quasi-periodic travelling gravity–capillary waves

We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.

97 MATHEMATICS AND COMPUTING↗