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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

System size and energy dependence of the mean transverse momentum fluctuations at the LHC

Event-by-event fluctuations of the event-wise mean transverse momentum, $\langle$p T $\rangle$, of charged particles produced in proton–proton (pp) collisions at $\sqrt{s}$ = 5.02 TeV, Xe–Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV, and Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are studied using the ALICE detector based on the integral correlator $\langle$$\langle$Δp T Δp T $\rangle$$\rangle$. The correlator strength is found to decrease monotonically with increasing produced charged-particle multiplicity measured at midrapidity in all three systems. In Xe–Xe and Pb–Pb collisions, the multiplicity dependence of the correlator deviates significantly from a simple power-law scaling as well as from the predictions of the HIJING and AMPT models. The observed deviation from power-law scaling is expected from transverse radial flow in semicentral to central Xe–Xe and Pb–Pb collisions. In pp collisions, the correlation strength is also studied by classifying the events based on the transverse spherocity, S 0 , of the particle production at midrapidity, used as a proxy for the presence of a pronounced back-to-back jet topology. Low-spherocity (jetty) events feature a larger correlation strength than those with high spherocity (isotropic). The strength and multiplicity dependence of jetty and isotropic events are well reproduced by calculations with the PYTHIA 8 and EPOS LHC models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A Modified Sand’s Time Incorporating Li-Ion Transport Across the SEI: Basis for Understanding Li Dendrite Formation and Li-Metal Battery Electrolyte Selection

Abstract Understanding the initiation of lithium dendrites remains elusive, largely due to the intricate role of the solid electrolyte interphase (SEI) which forms on the Li surface during electrodeposition. Many studies have utilized the classical Sand’s equation to estimate the onset time when lithium dendrites begin to form. The Sand’s equation provides the time when the cation (Li+) concentration at the electrode-electrolyte interface approaches zero under diffusion-limited conditions in galvanostatic Li electrodeposition. However, recent experimental studies have revealed that the observed lithium dendrite onset time deviates considerably from the Sand’s time. Here, we show that this deviation from classical theory is likely due to the transport of Li+ ions through the SEI - a transport limitation that is much more dominant in controlling dendrite formation. We develop a ‘modified’ Sand's equation, incorporating the SEI layer and the diffusional transport across it to predict Li dendrite onset times. To validate this approach, we conducted Li electrodeposition experiments at various current densities using two distinct organic electrolytes. Analysis of the results demonstrates that the modified Sand's equation provides a more accurate prediction of dendrite onset times, highlighting the importance of incorporating SEI into transport models of Li plating in next-generation rechargeable Li-metal batteries.

Ma, Yuanman (ORCID:0000000200444811)↗
DOE OSTI2025

Microstructure Scale Lithium-Ion Battery Modeling, Part IV: The Representativity of Microstructure Parameters and Electrochemical Response

Lithium-ion battery electrochemical models require an accurate description of the electrodes microstructures to be predictive, that can be achieved through nanoscale imaging. Such observations are however limited by their field of view (FOV), as they provide only a subset of the whole electrode volume that does not necessarily represent the whole electrode microstructure heterogeneity, and therefore can bias the analysis. A representativity analysis has been performed on the microstructure parameters and, in a novel way, on the full cell electrochemical response to evaluate the predictions representativeness, and thus relevance, of a microstructure scale electrochemical model. The microstructure parameter deviation propagations to the electrochemical response have been quantified for different charge rates. This defines a threshold for the microstructure parameters FOV for a desired maximum deviation of the electrochemical response. Electrochemical model shows cell representative section areas are increasing with C-rate, due to higher in-plane heterogeneities, indicating larger FOVs are required specifically for fast charge modeling. Representativity analysis determines a cell FOV of 144.4 × 154.4 μm 2 is large enough to establish a convergence on the representative section areas for low-intermediate C-rate (≤2.5 C), therefore positively concludes on the model representativeness for these rates, but is not large enough to conclude for higher rates.

25 ENERGY STORAGE↗
DOE OSTI2025

Microstructure Scale Lithium-Ion Battery Modeling: Part II. On In-Plane Heterogeneities and the Mechanisms that Regulate Them

Li-ion batteries performance and degradation are typically modeled at the macroscopic scale, that is neglecting in-plane heterogeneities that can arise from non-uniform electrode microstructures. Herein, a microstructure scale electrochemical model is used to quantify the impact of microstructure heterogeneity on cell performance during fast charging. The model predicts the electrolyte and solid concentration in-plane standard deviation can reach, respectively, ≈200 mol·m −3 and 6–7 kmol·m −3 locally. Further, the intercalation current density in-plane relative standard deviation can reach extremely high values, around 100% in the cathode and well above 100% in the anode graphite. These denote highly non-uniform lithiation rates and material utilization within each slice of the microstructure along the cell thickness. Non-uniform curvatures, at the particle scale (surface roughness) and between particles (size distribution), were found to initiate these in-plane heterogeneities, while an OCP-induced mechanism subsequently regulates them. The present model provides new insights into small length scale heterogeneity impact on battery performance not available with standard macro-scale/P2D modeling.

25 ENERGY STORAGE↗
DOE OSTI2025

Open-Source Ambient-Signal-Based Inertia Monitoring Tool for Power systems [SWR-25-59]

This script, developed by NREL, implements an inertia estimation algorithm using a sliding window approach. The inertia (H) is estimated based on frequency deviations and active power deviations, utilizing the swing equation from power system dynamics. An example application is provided using the WECC 240-bus system.

Peng, Jiangkai [National Renewable Energy Laborato↗
DOE OSTI2025

Autonomous Anomaly Detection For Continuous Streams

The code implements the Isolation Forest (IFML) algorithm within the digital twin (DT) of the AGN-201 nuclear reactor. The DT captures real-time operational data including control rod positions, reactor power, and temperature. The IFML model isolates anomalies by detecting patterns that deviate from expected operational behavior. The algorithm recursively partitions the data and assigns anomaly scores based on the isolation of rare and different events. By tuning parameters specific to the reactor’s operational data, the IFML identifies deviations such as unauthorized material insertions or reactor reactivity shifts. The system streams data using LabView and integrates with the DeepLynx data warehouse for anomaly processing.

Trevino, Eduardo↗
DOE OSTI2025

Round Robin Analysis of Uranium Isotopics on Cotton Swipes Measured Using Microextraction-Based Sampling Versus Conventional Bulk Analysis

A comparison of microextraction sampling methods to directly analyze uranium isotopics on cotton swipes was performed concurrently with traditional bulk-processing methods. For the microextraction sampling approach, two different detection platforms were evaluated, a quadrupole-based inductively coupled plasma mass spectrometer (ICP-MS) and the liquid sampling-atmospheric pressure glow discharge (LS-APGD) coupled to an Orbitrap mass spectrometer. Results presented from this innovative sampling approach (i.e., microextraction) are compared with a more traditional approach employed for analysis of cotton-based environmental swipes, namely bulk ashing/digestion, separation, and subsequent analysis by high-precision multi-collector ICP-MS. Overall, the microextraction approach proved to be a reliable and accurate means to determine isotopic ratios of uranium collected on cotton swipes. The ICP-MS-based detection had relative standard deviations of <0.65% for the major isotopic determinations, whereas the LS-APGD-Orbitrap method had relative standard deviations of <3%. The percent relative difference for the 235 U/ 238 U ratios, in comparison to the expected values, was <1% for ICP-MS and <4% for the microplasma-Orbitrap method. Additionally, the microextraction ICP-MS accurately (<2%) and precisely (<5%) determined the minor isotopic compositions (i.e., 234 U/ 238 U and 236 U/ 238 U).

ICP-MS↗
DOE OSTI2026

Terrestrial laser scanning data (Levels 0 and 1) for Pasoh, Malaysia, Sep 2024

This data package contains data from terrestrial laser scanning (TLS) at the Pasoh Forest Reserve, Malaysia. The Pasoh Forest Reserve is a facility of the Forest Research Institute Malaysia, and contains evergreen lowland dipterocarp forest. The Next-Generation Ecosystem Experiments Tropics (NGEE-Tropics) study areas at Pasoh were established to study how different species respond to climatic variation and soil water availability. Two study areas were chosen representing different topography and species. The TLS data archived here were collected to provide detailed, three-dimensional information about forest structure. Specifically, data were collected to allow tree-level characterization of woody structure and leaf area for 12 focal trees with FloraPulse and sap flux sensors, facilitating estimation of woody biomass and leaf area to allow upscaling of water content and transpiration data to the tree-level. Scan positions were not selected to provide consistent data for non-focal trees with the study areas. This data package contains the following data: - High-level files document further details of the campaign and data package: 1_CampaignSummary.csv provides details about the campaign and study site, 2_ScanAreasDetail.csv provides details about each separate scan area (groups of scans post-processed into a single point cloud), 3_TerrestrialLidarSensor.csv provides further technical details about the Riegl VZ-400i TLS sensor, TLS_CSV_dd.csv is a CSV Data Dictionary providing information about the fields in CSV files following the ESS-DIVE CSV File Formatting Guidelines Reporting Format, TLS_flmd.csv is a File Level Metadata file providing information about each file in the data package following the ESS-DIVE File Level Metadata Reporting Format, and README.txt is a text file describing the overall project and file structure. - Level 0 data are the raw data (.PROJ folders) as recorded by the Riegl VZ-400i TLS instrument before scan co-registration and post-processing with the Riegl's proprietary RiSCAN PRO software, which requires a license. - Level 1 data contain post-processed, co-registered data from each scan area. The "PointClouds" folder for each scan area contains a .las file with 1 cm resolution point cloud data exported from RiSCAN PRO. These are the main files likely to be of interest to most users and can be further processed with any software capable of manipulating .las files (e.g. Python, R CloudCompare). The "Project Information" folder contains log files from post-processing in RiSCAN PRO that may be of interest to users who want to see detailed records of post-processing, including all PDF reports generated by RiSCAN PRO. The "ScanPositions" folder contains information about the final position of all TLS scans, after post-processing, in multiple formats. The file ScanPositions_*.csv provides final geo-referenced scan positions, and the file SOP_backup_*.csv can be used in RiSCAN PRO to restore the co-registered scan positions if users wish to re-process raw data (Level 0 .PROJ folders) with RiSCAN PRO software (e.g., subsample to a different resolution, exclude a certain scan position, or apply different filters on reflectance or deviation values) without redoing time-consuming co-registration steps.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Terrestrial laser scanning data (Levels 0 and 1) from Urban Biogeochemistry Pilot Project sites, Knoxville, Tennessee, Jul 2024 - Jul 2025

This data package contains data from terrestrial laser scanning (TLS) at five urban park sites in Knoxville, Tennessee, USA. All parks include open-grown and/or closed-canopy trees and mixed nearby land use. These study sites were established as part of the Urban Biogeochemistry Pilot Project, which has an overall goal of better understanding how hydrobiogeochemical cycling is altered within the human environment. These five sites represent a gradient of urbanization, and were instrumented to understand hydrological and biogeochemical cycling (e.g., soil moisture, soil physical properties and biogeochemistry, tree transpiration, species type). The TLS data archived here were collected to provide detailed, three-dimensional information about forest structure. Specifically, data were collected to allow tree- and stand-level characterization of woody structure and leaf area. TLS scans were placed to capture the area around trees with sap flow sensors, and as much of a 50 m radius area around the meteorological station as possible given site property limits. Derived products will allow upscaling of water content and transpiration data. This data package contains the following data: - High-level files document further details of the campaign and data package: 1_CampaignSummary.csv provides details about the campaign and study site, 2_ScanAreasDetail.csv provides details about each separate scan area (groups of scans post-processed into a single point cloud), 3_TerrestrialLidarSensor.csv provides further technical details about the Riegl VZ-400i TLS sensor, TLS_CSV_dd.csv is a CSV Data Dictionary providing information about the fields in CSV files following the ESS-DIVE CSV File Formatting Guidelines Reporting Format, TLS_flmd.csv is a File Level Metadata file providing information about each file in the data package following the ESS-DIVE File Level Metadata Reporting Format, and README.txt is a text file describing the overall project and file structure. - Level 0 data are the raw data (.PROJ folders) as recorded by the Riegl VZ-400i TLS instrument before scan co-registration and post-processing with the Riegl's proprietary RiSCAN PRO software, which requires a license. - Level 1 data contain post-processed, co-registered data from each scan area. The "PointClouds" folder for each scan area contains a .las file with 1 cm resolution point cloud data exported from RiSCAN PRO. These are the main files likely to be of interest to most users and can be further processed with any software capable of manipulating .las files (e.g. Python, R CloudCompare). The "Project Information" folder contains log files from post-processing in RiSCAN PRO that may be of interest to users who want to see detailed records of post-processing, including all PDF reports generated by RiSCAN PRO. The "ScanPositions" folder contains information about the final position of all TLS scans, after post-processing, in multiple formats. The file ScanPositions_*.csv provides final geo-referenced scan positions, and the file SOP_backup_*.csv can be used in RiSCAN PRO to restore the co-registered scan positions if users wish to re-process raw data (Level 0 .PROJ folders) with RiSCAN PRO software (e.g., subsample to a different resolution, exclude a certain scan position, or apply different filters on reflectance or deviation values) without redoing time-consuming co-registration steps.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Importance of Considering Near-Surface Attenuation in Earthquake Source Parameter Estimation: Insights from Kappa at a Dense Array in Oklahoma

ABSTRACT Separating earthquake source spectra from propagation effects is challenging. The propagation effect contains a site-dependent term related to the high attenuation of shallow sediments. Neglecting the site-dependent attenuation can cause large biases and scattering in the corner-frequency (fc) estimates, resulting in significant stress-drop deviations. In this study, we investigate shallow attenuation at the LArge-n Seismic Survey in Oklahoma (LASSO) and site-related biases and scattering in source parameter measurements due to simplified attenuation models. We measure the high-frequency spectral decay parameter kappa on the vertical acceleration spectra of regional earthquakes (125 km away). The site-dependent kappa (κ0,acc) suggests that attenuation increases rapidly at shallow depth and is highly site-dependent. 10%–75% of the attenuation is site-dependent for S waves and even larger for P waves. The quality factor for S waves (QS) ranges from 10 to 100 in the upper 400 m. QP for P waves is mostly below 10 within the same depth. The Quaternary sediments tend to be more attenuating (QS<30), but the Permian rocks also can have high attenuation. We demonstrate that using a non-site-dependent attenuation model in single-spectra fitting leads to large scattering in fc estimates among stations with apparent good fits. The apparent fc can significantly deviate when the range of site-dependent kappa is large or with a higher assumed source spectral fall-off rate n. The biases in apparent fc depend on site condition and distance; however, the correlation between fc and these factors might not be obvious, depending on model assumptions. An apparent increase of stress drop with magnitude in a previous study for local microearthquakes (1.3

Chang, Hilary↗
DOE OSTI2025

Factors That Influence Variability in Stress-Drop Measurements Using Spectral Decomposition and Spectral-Ratio Methods for the 2019 Ridgecrest Earthquake Sequence

Stress drop is a fundamental parameter related to earthquake source physics, but is hard to measure accurately. To better understand how different factors influence stress-drop measurements, we compare two different methods using the Ridgecrest stress-drop validation data set: spectral decomposition (SD) and spectral ratio (SR), each with different processing options. Here, we also examine the influence of spectral complexity on source parameter measurement. Applying the SD method, we find that frequency bandwidth and time-window length could influence spectral magnitude calibration, while depth-dependent attenuation is important to correctly map stress-drop variations. For the SR method, we find that the selected source model has limited influence on the measurements; however, the Boatwright model tends to produce smaller standard deviation and larger magnitude dependence than the Brune model. Variance reduction threshold, frequency bandwidth, and time-window length, if chosen within an appropriate parameter range, have limited influence on source parameter measurement. For both methods, wave type, attenuation correction, and spectral complexity strongly influence the result. The scale factor that quantifies the magnitude dependence of stress drop show large variations with different processing options, and earthquakes with complex source spectra deviating from the Brune-type source models tend to have larger scale factor than earthquakes without complexity. Based on these detailed comparisons, we make a few specific suggestions for data processing workflows that could help future studies of source parameters and interpretations.

58 GEOSCIENCES↗
DOE OSTI2026

Time-of-Flight energy measurements with BPMs

The energy of a bunched non-relativistic ion beam can be deduced from measuring the beam phases in neighboring Beam Position Monitors (BPMs). This report presents estimations on implementation of such a procedure at PIP-II H- linac being constructed at Fermilab. In part, the case when the flight time between BPMs is larger than the period of BPM frequency is considered in detail. When the absolute BPM phase calibration is not available, the BPM phase information can be used to trace deviations of the beam energy from the desired value. Such “energy deviation” parameter is operationally implemented at the transfer line between 400 MeV Linac and the Booster, and its analog is expected to be used in the transfer line from PIP-II as well.

Shemyakin, Alexander [Fermilab] (ORCID:00000001501↗
DOE OSTI2025

Elucidating the Dynamics of Electroweak Symmetry Breaking through Study of High-Multiplicity Boson Final States at the LHC

To understand the full story of the electroweak symmetry breaking (EWSB) and how the universe arrived at today’s universe, the structure of the Higgs potential needs to be probed. We must carefully select and study processes at the LHC that are sensitive to the Higgs potential. In this context, longitudinal vector boson scattering (VBS) processes, V L V L →V L V L , and di-Higgs production, including V L V L →HH at the LHC have been studied for any potential deviation from SM prediction. However, many classes of models beyond the Standard Model (BSM) may result in the 2→2 process being perfectly well-behaved and SM-like but show interesting deviations in 2→3, 2→4, or 2→n(3) processes. If we are to complete the mission objectives the P5 laid out, then a large swath of 2→n(3) must be thoroughly searched and checked. The research supported by this award used data collected at the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) to explore VBS produced VVH process in the semi-merged channel. In addition, in the electroweak sector, there are open questions in the multi-gauge boson couplings and the Higgs couplings to the gauge bosons. The research supported by the award also studied the triboson production WWZ process at the LHC, which is a crossed diagram of a VBS process. During the funded period of 9 months, the analysis designs have been finalized.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Final Technical Report on Investigation of Short-range Ordering in Transition Metal Compounds by Diffuse Scattering

Future energy needs and sustainability require new materials with novel properties for such applications as energy production, storage and transport and microelectronics. Quantum materials with several competing interactions at the electronic level offer tremendous opportunity to discover, design and tune properties for such applications. Although it has been recognized that small deviations in atomic positions, driven by the competing electronic interactions, in crystalline materials can have significant impact on properties, it remains a challenge to accurately characterize such deviations (short-range order) due to the lack of advanced instruments and analysis tools to characterize them. This project used the powerful neutron and x-ray scattering instruments recently developed at the DOE user facilities to address this challenge. New methods and efficient analysis tools were employed to uncover the hidden ordering that is behind the unique properties of transition metal compounds. One example of hidden order revealed by this project comes from vanadium (IV) oxide (VO 2 ) and related compounds. The project found that the chemical bonds in VO 2 compete against each other, unlike most crystalline compounds where the chemical bonds cooperate to yield the ordered structure. This helps explain why different measurements yielded different, competing pictures about the nature of VO 2 , which has led to disagreement about where its physical properties come from. Another example from this project of hidden ordering comes from a class of compounds known as condensed Chevrel phases, which are superconducting compounds that are generally believed to be non-magnetic. The neutron scattering methods used in this project revealed evidence of magnetism, which usually does not coexist with superconductivity. In this case, magnetism is believed to be one part of a special type of electronic behavior that can occur in compounds that have one-dimensional bonding character.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bounds on Lorentz Violation Parameters in the DUNE Experiment

The Standard Model (SM) has been highly successful in describing fundamental interactions, yet phenomena like neutrino oscillations point to physics beyond its framework. Among the proposed extensions, Lorentz invariance violation (LIV) stands out as a compelling possibility. Long-baseline neutrino experiments such as DUNE, with its 1300 km baseline, offer a promising setting to test LIV effects with high precision. In this work, we evaluate DUNE s sensitivity to LIV by analyzing event rates and oscillation probabilities using the GLoBES framework. A custom implementation of LIV parameters was employed to derive bounds on the aa and cc matrices, identifying the parameter values that lead to a 10% deviation from the standard oscillation probability. Our results show partial agreement with previous studies for the aa parameters, while deviations in the cc parameters highlight the impact of differing methodologies and sensitivities. These findings reinforce the relevance of LIV searches and motivate further theoretical and experimental efforts in this direction.

Cruz, Thiago. [Tech. Fed. Parana U.]↗
DOE OSTI2025

Time-of-Flight Energy Measurements With BPMs

The energy of a bunched non-relativistic ion beam can be deduced from measuring the beam phases in neighbouring Beam Position Monitors (BPMs). This report discusses implementation of such a procedure at the PIP-II H- linac being constructed at Fermilab. The case when the flight time between BPMs is longer than the period of BPM frequency is considered in more detail. When absolute BPM phase calibration is not available, the BPM phase information can be used to track deviations of the beam energy from the de-sired value. Such energy deviation parameter is operationally implemented at the transfer line between 400 MeV Linac and the Booster, and its analog is expected to be used in the transfer line from PIP-II as well.

Shemyakin, Alexander V. [Fermilab] (ORCID:00000001↗
DOE OSTI2024

LES and RANS Spray Combustion Analysis of OME 3-5 and n-Dodecane

Clean-burning oxygenated and synthetic fuels derived from renewable power, so-called e-fuels, are a promising pathway to decarbonize compression–ignition engines. Polyoxymethylene dimethyl ethers (PODEs or OMEs) are one candidate of such fuels with good prospects. Their lack of carbon-to-carbon bonds and high concentration of chemically bound oxygen effectively negate the emergence of polycyclic aromatic hydrocarbons (PAHs) and even their precursors like acetylene (C 2 H 2 ), enabling soot-free combustion without the soot-NO x trade-off common for diesel engines. The differences in the spray combustion process for OMEs and diesel-like reference fuels like n-dodecane and their potential implications on engine applications include discrepancies in the observed ignition delay, the stabilized flame lift-off location, and significant deviations in high-temperature flame morphology. For CFD simulations, the accurate modeling and prediction of these differences between OMEs and n-dodecane proved challenging. This study investigates the spray combustion process of an OME 3 − 5 mixture and n-dodecane with advanced optical diagnostics, Reynolds-Averaged Navier–Stokes (RANS), and Large-Eddy Simulations (LESs) within a constant-volume vessel. Cool-flame and high-temperature combustion were measured simultaneously via high-speed (50 kHz) imaging with formaldehyde (CH 2 O) planar laser-induced fluorescence (PLIF) representing the former and line-of-sight OH* chemiluminescence the latter. Both RANS and LES simulations accurately describe the cool-flame development process with the formation of CH 2 O. However, CH 2 O consumption and the onset of high-temperature reactions, signaled by the rise of OH* levels, show significant deviations between RANS, LES, and experiments as well as between n-dodecane and OME. A focus is set on the quality of the simulated results compared to the experimentally observed spatial distribution of OH*, especially in OME fuel-rich regions. The influence of the turbulence modeling is investigated for the two distinct ambient temperatures of 900 K and 1200 K within the Engine Combustion Network Spray A setup. The capabilities and limitations of the RANS simulations are demonstrated with the initial cool-flame propagation and periodic oscillations of CH 2 O formation/consumption during the quasi-steady combustion period captured by the LES.

CFD↗
DOE OSTI2025

Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. II. Locality of Gravitoturbulence, Clumpy Spirals, and Implications for Observable Substructure

Spiral perturbations in a gravitationally unstable accretion disk regulate disk evolution through angular momentum transport and heating and provide an observational signature of gravitational instability (GI). We use global 3D simulations to systematically characterize and understand these spiral perturbations. The spiral perturbations and the resulting transport are overall insensitive to the cooling type, with the exception that radiative cooling, especially in the optically thick regime, reduces the amplitude of temperature perturbations. Spiral perturbations are localized around corotation, allowing transport to be approximated by a local α viscosity to zeroth order in aspect ratio (H/R), but only after averaging over multiple orbits in time and/or multiple scale heights in space. Meanwhile, large-amplitude perturbations from strong gravitoturbulence can cause $\mathcal{O}$(α 1/2 ) deviation in the cooling rate of the disk. We develop empirical prescriptions for the angular momentum transport, heating, and cooling in a gravitoturbulent disk that capture the deviation from a viscous, unperturbed disk to first order in H/R and α 1/2 . The spiral perturbations in saturated gravitoturbulence are clumpy, with dense clumps forming through the nonlinear coupling between multiple modes at different m. Observationally, the clumpy gravitoturbulence produced by saturated GI can be mistaken with observational noise or embedded companions, especially under finite resolution. Meanwhile, grand-design spirals with m-fold symmetry may be uncommon among disks in saturated gravitoturbulence, and we speculate that they may instead be a signature of recently triggered or decaying GI.

Gravitational instability↗