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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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Evaluation of a coastal acoustic buoy for cetacean detections, bearing accuracy and exclusion zone monitoring

Abstract There is strong socio‐political support for offshore wind development in US territorial waters and construction is planned off several east coast states. Some of the planned development sites coincide with important habitat for critically endangered North Atlantic right whales. Both exclusion zones and passive acoustic monitoring are important tools for managing interactions between marine mammals and human activities. Understanding where animals are with respect to exclusion zones is important to avoid costly construction delays while minimizing the potential for negative impacts. Impact piling from construction of hundreds of offshore wind turbines likely require exclusion zones as large as 10 km. We have developed a three‐hydrophone passive acoustic monitoring system that provides bearing information along with marine mammal detections to allow for informed management decisions in real‐time. Multiple units form a monitoring system designed to determine whether marine mammal calls originate from inside or outside of an exclusion zone. In October 2021, we undertook a full system validation, with a focus on evaluating the detection range and bearing accuracy of the system with respect to right whale upcalls. Five units were deployed in Mid‐Atlantic waters and we played more than 3500 simulated right whale upcalls at known locations to characterize the detection function and bearing accuracy of each unit. The modelled results of the detection function error were then used to compare the effectiveness of a bearing‐based system to a single sensor that can only detect a signal but not ascertain directivity. Field trials indicated maximum detection ranges from 4–7.3 km depending on source and ambient noise levels. Simulations showed that incorporating bearing detections provide a substantial improvement in false alarm rates (6 to 12 times depending on number of units, placement and signal to noise conditions) for a small increase in the risk of missed detections inside of an exclusion zone (1%–3%). We show that the system can be used for monitoring exclusion zones and clearly highlight the value of including bearing estimation into exclusion zone monitoring plans while noting that placement and configuration of units should reflect anticipated ambient noise conditions.

17 WIND ENERGY↗
DOE OSTI2020

Nevada National Security Site E-Tunnel Wastewater Disposal System Quarterly Monitoring Report, Water Pollution Control Permit NEV 96021 (First Quarter Calendar Year 2020)

This report includes the results of monthly inspections and monitoring for January, February, and March 2020. Monthly inspections and monitoring were conducted on January 15, February 12, and March 17, 2020. Inspections include a visual assessment of the berms, ponding, water levels relative to the overflow pipes, tunneling or burrowing into the berms, soil conditions on and around the berms, erosion or sloughing of the slopes of the berms, seeps at the toe of the berms, deep-rooting botanicals on the berms, and fencing. Monthly monitoring includes measurements of the instantaneous flow rate, hydrogen ion activity (pH), and specific conductance of the E-Tunnel Wastewater Disposal System discharge.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

E-Tunnel wastewater discharge permit quarterly monitoring report. Water pollution control permit Nev 96021, third quarter 2020

Monitoring and sampling activities are performed at the E-Tunnel Wastewater Disposal System (ETDS ) in accordance with the requirements of Water Pollution Control (WPC) Permit NEV 96021, Revision 1, which is effective October 1, 2013. Although the end date of the WPC permit is September 30, 2018, the Nevada Division of Environmental Protection (NDEP), in a letter dated September 21, 2018, provided guidance that indicated the WPC Permit NEV 96021, Revision 1, is in effect until NDEP notifies the U.S. Department of Energy, National Nuclear Security Administration Nevada Field Office otherwise. This QMR includes the results of monthly inspections and monitoring for July, August, and September 2020. Monthly inspections and monitoring were conducted on July 21, August 19, and September 16, 2020. Inspections include a visual assessment of the berms, ponding, water levels relative to the overflow pipes, tunneling or burrowing into the berms, soil conditions on and around the berms, erosion or sloughing of the slopes of the berms, seeps at the toe of the berms, deep-rooting botanicals on the berms, and fencing. Monthly monitoring includes measurement s of the instantaneous flow rate, hydrogen ion activity (pH), and specific conductance of the ETDS discharge. The report will be submitted to the State of Nevada.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Non-Invasive Biophysical Techniques to Monitor the Structural Plasticity of the Photosynthetic Machinery of Live Diatom Cells

The photosynthetic performance of diatoms depends largely on the organization and structural flexibility of their thylakoid membranes, the densely packed, highly organized membrane vesicles in which light reactions of photosynthesis occur. Different regulatory mechanisms that fine tune the photosynthetic functions affect the organization of the photosynthetic machinery at different levels of structural complexity, from the level of individual protein complexes to the macroarray of membrane proteins and the remodeling of the entire thylakoid membrane system. To monitor these reorganizations, non-invasive techniques are of special value. In this chapter, we focus our attention on three of these techniques, which have been demonstrated to provide unique and useful information on the structure and structural and functional plasticity of live diatom cells: (i) circular dichroism (CD) spectroscopy, which has provided unique information on the chiral (macro-)organization of protein complexes and on their rapid, reversible reorganizations, fine-tuning the light-harvesting processes, as well as on variations in the short-range excitonic interactions in the antenna complexes; (ii) small-angle neutron scattering (SANS), which has been used to determine the periodic organization of the thylakoid membranes and to monitor reversible ultrastructural changes on the time-scale of minutes, induced by variations in the environmental conditions such as changes in temperature or light intensity; and (iii) electrochromic shift absorbance transients (ΔA ECS ), a spectroscopic tool which has been shown to be capable of identifying distinct functional groups of the light-harvesting carotenoid fucoxanthin in different diatoms and in cells exposed to different light intensities. Future use of these techniques will most certainly contribute to the deeper understanding of key regulatory mechanisms of photosynthesis in diatoms.

Szabo, Milan↗
DOE OSTI2021

Hybrid electric buses fuel consumption prediction based on real-world driving data

Estimating fuel consumption by hybrid diesel buses is challenging due to its diversified operations and driving cycles. Here, long-term transit bus monitoring data were utilized to empirically compare fuel consumption of diesel and hybrid buses under various driving conditions. Artificial neural network (ANN) based high-fidelity microscopic (1 Hz) and mesoscopic (5–60 min) fuel consumption models were developed for hybrid buses. The microscopic model contained 1 Hz driving, grade, and environment variables. The mesoscopic model aggregated 1 Hz data into 5 to 60-minute traffic pattern factors and predicted average fuel consumption over its duration. The prediction results show mean absolute percentage errors of 1–2% for microscopic models and 5–8% for mesoscopic models. The data were partitioned by different driving speeds, vehicle engine demand, and road grade to investigate their impacts on prediction performance.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

A Machine Learning Model for Predicting Composition of Catalytic Coprocessing Products from Molecular Beam Mass Spectra

Demand for the development of an automated and integrated refining process for biofuels has increased in recent years due to the lack of generalized process inspection tools. In bio-oil upgrading processes, all process variables are maintained based on the offline specification of intermediates and products. A lack of real-time product specifications in batch-wise monitoring can cause process failure and wasted resources. Therefore, there is a need for a fast and accurate intermediates/product specification tool that can be used for real-time specification to reduce waste and mitigate the risk of process failure. Here, to address this gap, we developed a machine learning (ML) model for predicting speciated bio-oil composition, including paraffin, iso-paraffins, olefins, naphthene, and aromatics. The model is trained using the mass spectra from upgraded products collected in the vapor phase before condensation and predicts the composition of the condensed product. Training ML models using raw mass spectra is challenging due to numerous overlapped peaks originating from different parent compounds. With this in mind, we propose a protocol that (i) transforms raw mass spectra to chemistry-inspired predefined features and (ii) trains decision tree-based models using these features. Our results show that the random forest model was robust against overfitting and had the highest accuracy compared to other models. Moreover, a stochastic ablation method determined the eight most significant features while maximizing the accuracy. Our protocol facilitates real-time compositional analysis of upgraded bio-oils and thus real-time process monitoring. Additionally, this protocol enables the rational design of efficient catalysts and the determination of optimal process conditions.

09 BIOMASS FUELS↗
DOE OSTI2021

First application of a digital mirror Langmuir probe for real-time plasma diagnosis

We report for the first time, a digital Mirror Langmuir Probe (MLP) has successfully sampled plasma temperature, ion saturation current, and floating potential together on a single probe tip in real time in a radio-frequency driven helicon linear plasma device. This is accomplished by feedback control of the bias sweep to ensure a good fit to I–V characteristics with a high frequency, high power digital amplifier, and field-programmable gate array controller. Measurements taken by the MLP were validated by a low speed I–V characteristic manually collected during static plasma conditions. Plasma fluctuations, induced by varying the axial magnetic field($\widetilde{f}$ = 10 Hz), were also successfully monitored with the MLP. Further refinement of the digital MLP pushes it toward a turn-key system that minimizes the time to deployment and lessens the learning curve, positioning the digital MLP as a capable diagnostic for the study of low radio-frequency plasma physics. These demonstrations bolster confidence in fielding such digital MLP diagnostics in magnetic confinement experiments with high spatial and adequate temporal resolution, such as edge plasma, scrape-off layer, and divertor probes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Weather data at The Morton Arboretum 2017-2023

We have been monitoring long-term weather patterns using two weather stations at The Morton Arboretum to link environmental conditions to tree growth and other tree responses. This data package contains weather data at The Morton Arboretum from 2017-08-23 to 2023-12-31; data is located in the "MortonWeatherData2017_2023.csv" file. The two weather stations are located on each side of The Arboretum (e.g., the Nursery station on the East side and the Ware Field station on the West side; the two weather stations are 3.23 km apart and coordinates are included in the "Location_metadata.csv" file). Measured variables include rain accumulation, air temperature, relative humidity, three soil moisture/temperature measurements at various depths (10, 30, and 50 cm for the Nursery weather station, and 10, 25, and 50 cm for the Ware Field), solar radiation, saturation vapor pressure, and vapor pressure deficit.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Initial development of a method for correlating indentation test results to damage accumulation in high temperature structural materials

This report describes an experimental approach based on microindentation creep or relaxation tests for assessing the remaining creep life of a sample material. The objective for this experimental program is to complement the development of passively loaded in situ surveillance specimens. These surveillance specimens could be placed in future advanced reactors to assess the degradation of structural properties, primary creep and creep-fatigue life, when the material is exposed to actual reactor operating conditions. The specimens and the corresponding indentation test protocol could form the basis of a structural health monitoring program designed to ensure the safe continued operation of the component given the relatively unknown effect of the reactor coolant chemistry, radiation exposure, and other environmental effects on the material properties of the constituent structural materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

2021 Q1 Project Report: Optimized Bifacial PV Systems (Q1 FY2021 Project Report)

This project has four main technical objectives: 1) Develop and improve bifacial performance models by adding the capability to evaluate electrical behavior and performance of bifacial modules and arrays under realistic field conditions including irradiance variability caused by racking, module frame, and position in the array. 2) Instrument and monitor performance of fielded bifacial systems to validate performance models and to measure, analyze and publish on bifacial energy gain. These should include both research and commercial bifacial systems and cover a variety of deployment applications. 3) Evaluate optimal bifacial system designs using simulations leveraging high-performance computing, and also using full sized and miniaturized experimental field deployments. 4) Establish and contribute to international test standards for bifacial system performance, testing, and safety, and work with the community to establish installation and siting best practices.

42 ENGINEERING↗
DOE OSTI2022

WISP: Watching grid Infrastructure Stealthily through Proxies (Final Technical Report)

The complex interdependencies of cyber systems (sensors and communications), physical grids and associated electricity market operations make protecting electric power grids a significant challenge. The energy sector is constantly under new, targeted, advanced and dangerous cyber-attacks that have the potential to result in the loss of human life. These threats are further exacerbated by our need to modernize the grid. One focus of cyber security research in smart grids is the securing of the SCADA system through advanced intrusion detection systems (IDS) and bad data detection algorithms in state estimation. These methods either require full knowledge of the system topology and parameters or fail to understand the physical behaviors under attack. WISP (Watching grid Infrastructure Stealthily through Proxies) is designed to provide additional protection to the power grid using only publicly available data. In particular, WISP exploits the spatio-temporal nature of the real time locational marginal prices (LMPs), in conjunction with other information such as bids, weather, outages and load data to analyze anomalous power pricing behaviors and then correlate those observations to localize regions of interest and identify potential cyber events. WISP is non-intrusive as the tool is deployed as a service in the Cloud or on premise and provides reliable information to system operators for enhanced situational awareness, without impeding energy delivery functions. The WISP technology comprises three modules: the data-driven anomaly detection core, the vulnerability and risk analysis and the root cause analysis. The data-driven anomaly detection core performs the tasks of feature selection, anomaly detection and attack region localization. The vulnerability and risk analysis module provides system level information of the vulnerable variables and times, assisting the operators in selecting monitoring and protection nodes. The root cause analysis module takes the detection results and identifies potential operational conditions that contribute to the detected anomalies. In Phase I, we have demonstrated the feasibility and effectiveness of WISP. We developed a realistic electricity market simulator capable of generating normal and attack market data under various operational conditions. We developed a series of cyber-attack detection and analysis algorithms and evaluated them under multiple data sources. Finally, we integrated all modules into an end-to-end software, providing functions for data management, data analytics and visualization. Specifically, we have achieved: (i) real-time data acceptance from external utility interfaces with >99% acceptance rate; (ii) high performance anomaly detection algorithms with >98% detection accuracy and <0.1% false alarm rate; and (iii) ultra-low computing delay <50 milliseconds. Additionally, our team developed algorithms to identify the vulnerable variables in electricity market operations and root cause analysis functions to identify major contributors to the price spikes. These ancillary modules are necessary when deploying WISP in real world industry environment. In Phase II, we have demonstrated the effectiveness of WISP software on realistic largescale power systems. We performed red team testing for the Phase I WISP software and identified software vulnerabilities and implemented corresponding mitigation solutions. We adapted the electricity market simulator for the Texas synthetic 2000-bus system and generated datasets for the false data injection attacks. We created database and visualization interfaces for the Texas system and the ISO New England system. We performed software optimization in terms of operation efficiency, computing speed and detection accuracy. Finally, we tested the software on the Texas system and the ISO New England system and evaluated the detection performance. Overall, we achieved above 89% detection rate, below 3% false alarm rate and below 37 seconds of end-to-end detection delay.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Corrosion of U233-Doped Uranium Oxide using Microfluidics Methods

The aim of work this year has been to investigate the role of alpha (α)-radiation and hydrogen (H 2 ) on the corrosion of uranium oxide (UO 2 ) using a microfluidic device. The microfluidic device, termed the Particle-Attached Microfluidic Electrochemical Cell, (PAMEC), enables monitoring of the UO 2 electrochemical corrosion potential (E corr ) under different environments, including de-aerated conditions and in the presence of dissolved H 2 . The Si 3 N 4 window allows us to study morphological and chemical changes under an electron microscope. We have previously demonstrated that the PAMEC matches the results from bulk electrochemical tests with UO 2 [1]. We used the high specific activity uranium (U) isotope, 233 U, (t 1/2 = 160,000 years) incorporated into UO 2 , to generate a localized a-field. The objective of the experiments were to mimic the radiation environment that would be experience at the surface of aged spent nuclear fuel (SNF) during long-term geologic disposal under anoxic conditions. Wittman et al. [2] predicted that in the presence of a pure a-radiation field and under H 2 conditions, the concentration of the radiolytic oxidant H 2 O 2 would be suppressed or even eliminated. In a UO 2 corrosion experiment this would be exhibited through a lowering of the measured UO 2 corrosion potential compared to identical conditions in the absence of dissolved H 2 . We found that the predictions of Wittman and co-workers were supported and that the corrosion potential of the 233 U-doped UO 2 in solution lowered with presence of H 2 gas and increased in the absence of H 2 , when under anoxic conditions. The PAMEC experiments indicate that H 2 O 2 has been eliminated in a solution sparged with H 2 while exposed to an a-radiation field. The corrosion potential of the a-doped 233 U(10%)- 238 UO 2 in a solution sparged with Ar/H 2 matched the corrosion potential of 238 UO 2 in solution sparged with air. This clearly demonstrated that the H 2 O 2 had been eliminated and that the only oxidant present was O 2 in this system in complete agreement with the modeling results of Wittman et al. These results point to the need to improve the Fuel Matrix Degradation (FMD) Process Model training data set that is being used in the FMD surrogate model that is being developed for the repository program. The incorporation of realistic radiation chemistry will improve the scientific basis for the FMD Model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Melt Wire Analyses for the Colorado School of Mines (CSM 16-10584) Irradiation in ATR

PNNL project 74242 involves the analysis of neutron fluence monitors and melt wires irradiated in the Advanced Test Reactor (ATR) at Idaho National Laboratory in accordance with MPO 00236287 and Statement of Work No. 17370, Rev. 0, PNNL Analysis of NSUF Flux and Melt Wire Capsules. This report is for the Colorado School of Mines (CSM 16-10584) experiment which was conducted in position B5 of the ATR. Neutron fluence monitor results were reported in February 2021 in report Neutron Dosimetry for the Colorado School of Mines (CM 16-10584) Irradiation in ATR. This report presents the analyses of the melt wire capsules that were included along with the neutron fluence monitors. Each capsule was identified by the ID stamp on the bottom, then opened to assess the condition of the Pb and Zn-Al wires as well as the Bi powder. Pictures are included to illustrate the results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

How Earth System Models Can Inform Key Dimensions of Marine Food Security in the Alaskan Arctic

The Arctic is home to several groups of Indigenous Peoples, each with distinct ways of interacting with their environment and ways of life. Arctic, Indigenous Peoples’ food sovereignty is tightly linked with food security. Subsistence harvesting activities provide nutritious and culturally vital foods for Alaska Native households and communities. Climate change is causing rapid and more unpredictable shifts in environmental conditions that impact three of the key aspects of food security, availability, stability, and accessibility. While communities monitor the abundance and health of food webs and environments as part of subsistence harvest practices, anticipating major transformations and changes in these systems is challenging. We explored the potential of Earth System Model output in helping anticipate or project physical or ecosystem changes relevant to Alaska Indigenous peoples’ food security needs. Through examples of model products, that provide measures of accessibility and availability of marine resources, we show that modern models, such as the Energy Exascale Earth System Model presented here, can provide estimates of a broad suite of variables relevant to food security. We investigate how Earth System Model output could contribute to exploring questions related to aspects of Arctic food security such as accessibility and availability and highlight present model shortcomings that, if addressed, would move Earth System Models closer to being a useful tool for understanding environmentally driven changes to the availability and accessibility of harvestable food resources. Our example model-derived food security indicators illustrate how Earth System Model output could be combined with relevant, non-model, information sources; These model products are meant only as a starting point and a tool for engaging community members and to present, in an accessible way, the model’s potential utility, or current lack thereof, to rights holders and stakeholders concerned about food security. We are hopeful that with example products in hand, additional model development efforts will have a higher likelihood of success in achieving an iterative discussion with stakeholders regarding feasible and desired products.

Gibson, Georgina A.↗
DOE OSTI2023

Thermal Constraint Violations as a Result of Ambient Adjusted Transmission Line Ratings

Ambient Adjusted Ratings allow transmission line current ratings to be increased above static ratings while requiring minimal weather monitoring. However, Ambient Adjusted Ratings are still contingent on static parameters that may not match real world conditions. This poster examines how simulation methods can estimate the extent to which using Ambient Adjusted Ratings could result in the violation of a transmission line's thermal constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Biomass Carbon Removal and Storage (BiCRS)

To achieve the ambitious net-zero emission goal by 2050, it is vital to explore practical approaches for removing carbon dioxide from the air. One promising method is Biomass Carbon Removal and Storage (BiCRS). BiCRS combines the natural ability of plants to convert carbon dioxide into biomass with human engineering to store the biomass, or derived products (char), belowground where it won't decompose. By securely storing these materials underground, we can trap the carbon dioxide absorbed by the plants during their growth, thus aiding in carbon removal from the atmosphere. BiCRS not only addresses carbon emissions but also has co-benefits such as wildfire risk reduction by utilizing forest residues. It is essential to establish best practices to ensure accurate measurements of net carbon dioxide removed by BiCRS for policymakers, businesses and communities. Presently, there is a lack of consistent methods for calculating these removals, considering variables like plant type, storage conditions, and conditions for converting the biomass to other products for storage like char. This project develops guidelines for monitoring and reporting BiCRS activities, offering a dependable framework for measuring carbon dioxide removal, enabling adoption of transparent BiCRS approaches for making significant contributions to reducing carbon dioxide levels in the atmosphere.

biomass carbon removal and storage↗
DOE OSTI2026

Hydrogen Recombiner Catalyst Evaluations for Waste Storage

Radiolysis of water in nuclear waste storage generates hydrogen gas that can accumulate within sludge style waste and be rapidly released during agitation events, creating a significant flammability hazard. Engineering controls are therefore required to limit hydrogen concentrations during both quiescent storage and transient disturbances. Catalytic recombination of hydrogen in waste storage offgas is a proven mitigation strategy, maintaining hydrogen levels below flammability limits and managing sudden concentration spikes. Conventional recombiners rely on platinum and/or palladium catalysts, with development efforts focused on extending service life, increasing active surface area, and ensuring safe deployment in radioactive environments. Savannah River National Laboratory (SRNL) is evaluating a newly developed hydrogen recombiner catalyst from Canadian Nuclear Laboratories as a cost-effective and durable alternative for nuclear waste applications. Testing was conducted in SRNL’s Shielded Cells facility, which enables reduced-scale experimental modeling under radiation fields and near-use-case conditions relevant to radioactive waste storage. Catalyst performance was evaluated using a custom offgas characterization system designed for near-zero flow conditions. The experimental apparatus consisted of a gas-tight 2.7 L PTFE vessel equipped with temperature monitoring, gas flow controls, and a variable-speed mixer to simulate sludge agitation. Offgas composition was monitored using a dedicated gas chromatograph with argon carrier gas and a krypton internal standard. Measurements were obtained for an empty vessel, the vessel containing a well characterized radioactive tank waste sample, and the same configuration with the candidate catalyst installed. Results demonstrate that the new catalyst effectively reduced hydrogen concentrations in the offgas within the constraints of the experimental design. In addition to confirming catalytic activity, the testing provided valuable insights into experimental optimization and considerations for future performance evaluations. These findings support the potential scalability of the technology and highlight its applicability to broader nuclear waste management operations, offering improved safety and reduced operational costs through enhanced catalyst durability and lower replacement frequency.

Tener, Zachary P. [Savannah River National Laborat↗
DOE OSTI2022

Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number

Direct numerical simulations (DNS) are performed to investigate the spatial evolution of flat-plate zero-pressure-gradient turbulent boundary layers over long streamwise domains ( >300δ i , with δ i the inflow boundary-layer thickness) at three different Mach numbers, 2.5, 4.9 and 10.9, with the surface temperatures ranging from quasiadiabatic to highly cooled conditions. The settlement of turbulence statistics into a fully developed equilibrium state of the turbulent boundary layer has been carefully monitored, either based on the satisfaction of the von Kármán integral equation or by comparing runs with different inflow turbulence generation techniques. The generated DNS database is used to characterize the streamwise evolution of multiple important variables in the high-Mach-number, cold-wall regime, including the skin friction, the Reynolds analogy factor, the shape factor, the Reynolds stresses, and the fluctuating wall quantities. The data confirm the validity of many classic and newer compressibility transformations at moderately high Reynolds numbers (up to friction Reynolds number Re τ ≈1200 ) and show that, with proper scaling, the sizes of the near-wall streaks and superstructures are insensitive to the Mach number and wall cooling conditions. The strong wall cooling in the hypersonic cold-wall case is found to cause a significant increase in the size of the near-wall turbulence eddies (relative to the boundary-layer thickness), which leads to a reduced-scale separation between the large and small turbulence scales, and in turn to a lack of an outer peak in the spanwise spectra of the streamwise velocity in the logarithmic region.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗