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DOE OSTI2024

Outcomes of HPC User Support using a Science Gateway AI Assistant

High Performance Computing (HPC) is a vital resource for nuclear energy research, facilitating advanced simulations and complex modeling of the quantification and qualification of advanced reactor technology. However, a common gap in knowledge exists around utilizing HPC systems, particularly for nuclear energy researchers unfamiliar with specific HPC systems. A researcher may be well-versed in using one HPC system and understanding its associated processes. Yet, they might struggle when faced with a different HPC system and its unique processes. HPC support staff play a crucial role in addressing these challenges by providing educational resources and assisting users. However, they also face the challenge of maintaining these systems and ensuring they run efficiently for all users, a responsibility that can be challenging to scale effectively with the increasing demand and expansion of HPC systems. This paper addresses this knowledge gap with an artificial intelligence (AI) assistant that offers on-demand, site-specific HPC support for researchers. Idaho National Laboratory (INL) has deployed an AI assistant that is intended to supplement expert HPC support staff and assist nuclear energy researchers. This paper reports on a four-and-a-half-month study evaluating the integration of an AI assistant within a science gateway, with the goal of enhancing existing HPC support.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

An Integrated Framework for Risk Assessment of Safety-related Digital Instrumentation and Control Systems in Nuclear Power Plants: Methodology Refinement and Exploration

This report documents activities performed by Idaho National Laboratory (INL) during Fiscal Year (FY) 2023 for the U.S. Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program, Risk Informed Systems Analysis (RISA) Pathway, digital instrumentation and control (DI&C) risk assessment project. In FY 2019, the RISA Pathway initiated a project to develop a risk assessment strategy for delivering a technical basis to support effective, and secure DI&C technologies for digital upgrades/designs. A risk assessment-informed framework was proposed for this strategy, which aims to (1) provide a best-estimate, risk informed capability to quantitatively estimate the safety margin obtained from plant modernization, especially for safety-related DI&C systems, (2) support and supplement existing risk informed DI&C design guides by providing quantitative risk information and evidence, (3) offer a capability of design architecture evaluation of various DI&C systems, (4) assure the long-term safety and reliability of safety-related DI&C systems, and (5) reduce uncertainty in costs and support integration of DI&C systems in the plant. To achieve these technical goals, the LWRS-developed framework provides a means to address relevant technical issues by: (1) defining a risk informed analysis process for DI&C upgrade that integrates hazard analysis, reliability analysis, and consequence analysis, (2) applying risk informed tools to address common cause failures (CCFs) and quantify corresponding failure probabilities for DI&C technologies, particularly software CCFs, (3) evaluating the impact of digital failures at the component level, system level, and plant level, and (4) providing insights and suggestions on designs to manage the risks, thus to support the development and deployment of advanced DI&C technologies in nuclear power plants (NPPs). Adding diversity within a system or components is the primary means to eliminate and mitigate CCFs, but diversity also increases system complexity and may not address all sources of systematic failures. Optimization of diversity and redundancy applications for the safety-critical DI&C systems remains a challenge. To deal with the technical issues in addressing potential software CCFs in safety-related DI&C systems of NPPs and supporting relevant design optimization, the proposed framework provides: (a) A best-estimate, risk informed capability to address new technical digital issues quantitatively, focusing on software CCFs in safety-related DI&C systems of NPPs; (b) A common and a modularized platform for DI&C designers, software developers, cybersecurity analysts, and plant engineers to predict and prevent risk in the early design stage of DI&C systems; (c) Technical bases and risk informed insights to assist users address the risk informed alternatives for evaluation of CCFs in safety-related DI&C systems of NPPs; and (d) A risk informed tool that offers a capability of design architecture evaluation of various DI&C systems to support system design decisions in diversity and redundancy applications. The research and development efforts of this project in FY 2023 are focused on refining current methods on software CCF modeling and estimation and exploring additional innovative approaches to risk assessment of DI&C systems to enable a more comprehensive and complete assessment of various safety-related DI&C design architectures. The primary audience of this report are DI&C designers, engineers, and probabilistic risk assessment (PRA) practitioners. This includes stakeholders, such as the nuclear utilities and regulators who consider the deployment and upgrade of DI&C systems, DI&C software developers and reviewers, and cybersecurity specialists. It should be noted that all the analyses are performed for the demonstration of the methodology, not for the evaluation of an actual digital control system. Results are obtained based on limited design information and testing data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRSDate not supplied

Development of Stirling Convertors for Radioisotope and Fission Power Systems

NASA has been developing free-piston Stirling-cycle power convertors over the past 22 years for use in nuclear power systems that would provide electricity for space science missions to dark, dusty, or distant destinations where solar power is not practical. These nuclear power systems would generate heat from either the radioactive decay of isotopes or fission nuclear reactors. That heat would be converted to usable electricity using highly efficient Stirling convertors for a wide range of power needs needing 10s of watts to 50 kWe. NASA’s Radioisotope Power Systems (RPS) Program is maturing advanced thermoelectric and dynamic conversion technologies that would increase the system efficiency beyond what is currently possible using heritage systems to enable a larger number of robotic missions or higher power missions to solar system bodies of interest. The Dynamic Radioisotope Power Systems (DRPS) Project has matured prototype Stirling convertors to sufficiently increase the technology readiness level for infusion into flight development. Flexure and gas-bearing free-piston Stirling convertors were developed under contract by commercial partners and delivered to enable government evaluation. Gas-bearing designs have met performance and robustness requirements and were selected for flight development. This paper provides the status of SRSC test campaign and maturity level.

Dynamic↗

NASA NTRS2023

Development of Stirling Convertors for Radioisotope and Fission Power Systems

Dynamic↗

DOE OSTI2025

On the Recoverability of Reactor Dynamics from Point Kinetics Data using SINDYc

Data driven models for reactor dynamics tend to face a few notable challenges. First, the broad range of timescales present across the various feedback mechanisms. Next, high standards for safety and importance of model performance in all operational domains. Finally, the correlations between state variables observed in most transients leads to difficulties when methods attempt to attribute certain dynamic phenomena to a particular cause. The current paper seeks to support efforts towards incorporating physics knowledge into one particular data-driven method for finding reactor dynamics called ``Sparse Identification of Nonlinear Dynamics with Control (SINDYc). The incorporation of physical knowledge into SINDYc will help address the challenges listed above by giving the model an initial understanding of the system being modeled. The demonstration of an exact representation of a set of point reactor dynamics equations in SINDYc is provided. Then, this allows for further discussion with mathematical justification as to why SINDYc, and other data-driven methods, may be difficult to apply to nuclear reactor dynamics due to correlations in the state variables. A particularly useful result of this work is the set of candidate functions required in SINDYc to exactly represent the reactor dynamics under a point approximation. In the future, SINDYc can be integrated with point models for reactor dynamics before being applied to the physical system to yield higher accuracy.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Evaluation of Joint Cyber/Safety Risk in Nuclear Power Systems

This report presents an analysis of the Emergency Core Cooling System (ECCS) for a generic Boiling Water Reactor (BWR)-4 NPP. The Electric Power Research Institute (EPRI) developed Hazards and Consequences Analysis for Digital Systems (HAZCADS) process is applied to the ECCS and its subsystems to identify unsafe control actions (UCAs) which act as possible cyber events of concern. The analysis is performed for two design basis events: Small-break Loss of Coolant Accident (SLOCA) and general transients (TRANS), such as unintended reactor trip. In previous work, HAZCADS UCAs were combined with other cyber-attack analysis to develop a risk-informed approach; however, this was for a single system. This report explores advanced systems engineering modeling approaches to model the interactions between digital assets across multiple systems which may be targeted by cyber adversaries. The complex and interdependent design of digital systems has the potential to introduce emergent cyber properties that are generally not covered by hazard analyses nor formal nuclear Probabilistic Risk Assessment (PRA). The R&D and supporting analysis presented here explores approaches to predict and manage how interdependent system properties effect risk. To show the potential impact of a successful cyber-attack to formal PRA event tree probabilities, HAZCADS analysis was also used. HAZCADS was also used to model the automatic depressurization system (ADS) automatic actuation. This analysis extended to an integrated system analysis for common-cause failure (CCF). In this aspect, the HAZCADS analysis continued by analyzing plant design details for system connectivity in support of critical plant functions. A dependency matrix was developed to depict the integrated functionality of the interconnected systems. Areas of potential CCF are indicated. Future work could include adversary attack development to show how CCF could be caused, resulting in PRA events. Across the multiple systems that comprise the ECCS, the analysis shows that the change in such probabilities was very different between systems. This indicates that some systems have a larger potential risk impact from successful cyber-attack or digital failure, which indicates a need for these systems to have a higher priority for design and defensive measures. Furthermore, we were able to establish that a risk analysis using any arbitrary threat model establishes an ordering of components with regard to cyber-risk. This ordering can be used to influence the overall system design with an eye to lowering risk, or as a way to understand real-time risk to operational systems based on a current threat landscape. Expert knowledge of both the analysis process and the system being analyzed is required to perform a HAZCADS analysis. The need for a tiered risk analysis is demonstrated by the results of this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

sCO 2 Brayton Energy Conversion Customer Discovery

All energy production systems need efficient energy conversion systems. Current Rankine cycles use water to generate steam at temperatures where efficiency is limited to around 40%. As existing fossil and nuclear power plants are decommissioned due to end of effective life and/or societies’ desire for cleaner generation options, more efficient energy conversion is needed to keep up with increasing electricity demands. Modern energy generation technologies, such as advanced nuclear reactors and concentrated solar, coupled to high efficiency sCO 2 conversion systems provide a solution to efficient, clean energy systems. Leading R&D communities worldwide agree that the successful development of sCO 2 Brayton power cycle technology will eventually bring about large-scale changes to existing multi-billion-dollar global markets and enable power applications not currently possible or economically justifiable. However, all new technologies face challenges in the path to commercialization and the electricity sector is distinctively risk averse. The Sandia sCO 2 Brayton team needs to better understand what the electricity sector needs in terms of new technology risk mitigation, generation efficiency, reliability improvements above current technology, and cost requirements which would make new technology adoption worthwhile. Relying on the R&D community consensus that a sCO 2 power cycle will increase the revenue of the electrical industry, without addressing the electrical industry’s concerns, significantly decreases the potential for adoption at commercial scale. With a clear understanding of the market perspectives on technology adoption, including military, private sector, and utilities customers, the Sandia Brayton Team can resolve industry concerns for smoother development and faster transition to commercialization. An extensive customer discovery process, similar to that executed through the NSF’s I-Corp program, is necessary in order to understand the pain points of the market and articulate the value proposition of Brayton systems in terms that engage decision makers and facilitate commercialization of the technology.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS2010

Fission Surface Power System Initial Concept Definition

Under the NASA Exploration Technology Development Program (ETDP) and in partnership with the Department of Energy (DOE), NASA has embarked on a project to develop Fission Surface Power (FSP) technology. The primary goals of the project are to 1) develop FSP concepts that meet expected surface power requirements at reasonable cost with added benefits over other options, 2) establish a hardwarebased technical foundation for FSP design concepts and reduce overall development risk, 3) reduce the cost uncertainties for FSP and establish greater credibility for flight system cost estimates, and 4) generate the key products to allow NASA decision-makers to consider FSP as a preferred option for flight development. The FSP project was initiated in 2006 as the Prometheus Program and the Jupiter Icy Moons Orbiter (JIMO) mission were phased-out. As a first step, NASA Headquarters commissioned the Affordable Fission Surface Power System Study to evaluate the potential for an affordable FSP development approach. With a cost-effective FSP strategy identified, the FSP team evaluated design options and selected a Preliminary Reference Concept to guide technology development. Since then, the FSP Preliminary Reference Concept has served as a point-of-departure for several NASA mission architecture studies examining the use of nuclear power and has provided the foundation for a series of "Pathfinder" hardware tests. The long-term technology goal is a Technology Demonstration Unit (TDU) integrated system test using full-scale components and a non-nuclear reactor simulator. The FSP team consists of Glenn Research Center (GRC), Marshall Space Flight Center (MSFC) and the DOE National Laboratories at Los Alamos (LANL), Idaho (INL), Oak Ridge (ORNL), and Sandia (SNL). The project is organized into two main elements: Concept Definition and Risk Reduction. Under Concept Definition, the team performs trade studies, develops analytical tools, and formulates system concepts. Under Risk Reduction the team develops hardware prototypes and conducts laboratory-based testing.

Source record↗

DOE OSTI2022

Flexible Siting Criteria and Staff Minimization for Micro-Reactors

The economic potential of micro-reactors is vast and underestimated. Commonly-emphasized applications include niche markets such as remote communities, mines and military bases. However, micro-reactors could be used as flexible energy generators also for larger markets, such as mobile and containerized agriculture and manufacturing facilities, district heating, micro-grids for data centers, sea ports, airports and hospitals. The implication is that micro-reactors may have to be deployed also in non-remote locations. Successful implementation of micro-reactors needs a navigable and predictable licensing process, technology-appropriate siting restrictions, risk-informed emergency and safety requirements, and practical operating and maintenance requirements. The primary goal of this project was to develop siting criteria that are tailored to micro-reactors deployable in densely-populated areas, e.g., urban environments. To achieve that goal, we compared the characteristics of the MIT research reactor (MITR) with those of leading micro-reactor concepts (e.g., eVinci, USNC, Aurora), and evaluated whether and how the MITR design basis (e.g., inherent safety features, engineered safety systems, source term, emergency planning and emergency operating procedures) and associated regulations may be applicable to these new micro-reactors as well. What makes MITR a unique analogue in this context is its small power rating (6 MWt) and physical size, mode of operations (24/7 with a somewhat more commercial flavor than typical university reactors), and especially its urban location. Of course significant differences exist, such as mission (power production vs. research) and the reactor design itself. Leveraging the MITR experience, this project was able to generate criteria that will allow micro-reactors to realize their full economic potential as flexible heat and electricity generators for a diverse portfolio of applications in non-remote locations. As such, the outcome of this project might encourage investment in and use of micro-reactors. A second goal of the project was to conceptualize a model of operations for micro-reactors that would minimize the staffing requirements, and thus reduce the cost of electricity and heat generated by these systems. Here too our approach was to systematically review the MITR experience and requirements, as well as survey the innovations in autonomous control technologies and monitoring (e.g., advanced sensors, drones, robotics, AI) that would permit a dramatic reduction in staffing at future micro-reactor installations. The scope of work was expanded after the start date to include also an evaluation of micro-reactor security, using the so-called consequence-based analysis, and the development of a methodology to perform dynamic risk assessment for micro-reactors, using system theory and modeling and simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Benchmark Simulation of the Natural Convection Shutdown Heat Removal Test Facility Using SAM

Natural convection systems are a promising method to passively remove heat from reactor cavities during loss of forced flow accident scenarios. In this work at Argonne National Laboratory (ANL), a highly instrumented Natural Convection Shutdown Heat Removal Test Facility (NSTF) was used to demonstrate the effectiveness of air-cooled natural convection systems. In previous work, RELAP5-3D simulations were performed on this facility with favorable comparisons to experiment for mass flow rate, pressure drop, air temperature increase, and air velocity. Both experimental and simulation efforts with this facility present a useful opportunity to perform a benchmark study with the System Analysis Module (SAM). SAM is an advanced thermal-hydraulic system code currently in development at ANL for advanced non-light water reactor safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2016

Cryogenic Fluid Management Technology and Nuclear Thermal Propulsion

Cryogenic fluid management (CFM) is critical to the success of future nuclear thermal propulsion powered vehicles. While this is an issue for any propulsion system utilizing cryogenic propellants, this is made more challenging by the radiation flux produced by the reactor in a nuclear thermal rocket (NTR). Managing the cryogenic fuel to prevent propellant loss to boil off and leakage is needed to limit the required quantity of propellant to a reasonable level. Analysis shows deposition of energy into liquid hydrogen fuel tanks in the vicinity of the nuclear thermal engine. This is on top of ambient environment sources of heat. Investments in cryogenic/thermal management systems (some of which are ongoing at various organizations) are needed in parallel to nuclear thermal engine development in order to one day see the successful operation of an entire stage. High durability, low thermal conductivity insulation is one developmental need. Light weight cryocoolers capable of removing heat from large fluid volumes at temperatures as low as approx. 20 K are needed to remove heat leak from the propellant of an NTR. Valve leakage is an additional CFM issue of great importance. Leakage rates of state of the art, launch vehicle size valves (which is approximately the size valves needed for a Mars transfer vehicle) are quite high and would result in large quantities of lost propellant over a long duration mission. Additionally, the liquid acquisition system inside the propellant tank must deliver properly conditioned propellant to the feed line for successful engine operation and avoid intake of warm or gaseous propellant. Analysis of the thermal environment and the CFM technology development are discussed in the accompanying presentation.

Taylor, Brian D.↗

DOE OSTI2021

Multiphysics Modeling/Simulation Capabilities Based on MOOSE

Overview presentation of INL modeling and simulation efforts in support of NASA nuclear thermal propulsion design using MOOSE-based tools.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Qualification of System-Level Advanced Reactor Safety Analysis Software for Lead Systems: Final CRADA Report

SAS4A/SASSYS-1 is a simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced liquid-metal-cooled nuclear reactors. With its origin as SAS1A in the late 1960s, the SAS series of codes has been under continuous use and development for over forty-five years and represents a critical investment in safety analysis capabilities for the U.S. Department of Energy. Although SAS4A/SASSYS-1 was developed to support the analysis of any liquid-metal-cooled nuclear reactor, it has primarily been utilized to design and analyze Sodium Fast Reactors (SFRs). As a result, most of the qualification basis for SAS4A/SASSYS-1 has utilized sodium as a coolant and geometry descriptions that are prototypic of SFR configurations. In this project, which partnered with Westinghouse Electric Company, LLC, the initial foundation for a qualification basis centered on prototypic pool-type lead-cooled systems has been established, where the end goal is to extend support for utilization of SAS4A/SASSYS-1 in Lead Fast Reactor (LFR) licensing or authorization. This project included three fundamental technical tasks: LFR V&V test suite development (Task 1); qualification support for LFRs (Task 2); and LFR modeling capabilities evaluation and improvement (Task 3)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

TFR-2575 MARVEL Power Generation System (PGS)

This document contains the Level 3 requirements associated with the two subsystems of the Power Generation System (PGS) in the Microreactor Applications Research Validation and Evaluation (MARVEL) project.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Explainable tokamak-agnostic forecasting of fusion plasma instability via megahertz turbulent fluctuations

Scientific applications of artificial intelligence (AI) often remain limited by device-specific training and unexplained “black-box” approaches, creating fundamental barriers to cross-system generalization. This challenge is critical for nuclear fusion, where future reactors will have limited operational data for AI training. Here, we demonstrate that our neural network, trained solely on megahertz-scale turbulence measurements from one machine (DIII-D), forecasts Type-I edge localized mode (ELM) onsets in a different tokamak (KSTAR) through zero-shot weight transfer following physics-consistent preprocessing without device-specific retraining. Through an explainable AI framework combining gradient-weighted class activation mapping with physics validation, we reveal that our network can internalize physics relationships governing the ELM instabilities rather than memorizing device-specific patterns. The network perceives spatiotemporal features that correlate consistently with independently calculated instability growth rates, magnetohydrodynamic stability limits, and pedestal structure dynamics. Statistical analyses of dimensionally-reduced saliency features reveal the identical triangular features between the saliency representations, instability growth rates, and prediction probability across tokamaks, providing evidence that our forecasting system can show tokamak-agnostic generalization. This work contributes to a foundation for explainable scientific AI systems, where cross-system developments are essential for transcending traditional domain-specific constraints.

AI↗

DOE OSTI2022

Vision 0.3.2 Users Guide: Revision 0

Vision is a research software application developed by Pacific Northwest National Laboratory (PNNL) that incorporates the scientific and operational expertise for reviewing data from treaty monitoring radionuclide stations. These stations are part of a worldwide network to monitor for nuclear explosions, and the data they produce are critical to make the determination of whether a sample is from a nuclear explosion or some other source (i.e., nuclear reactor or medical isotope production facility). Stations deliver their measurements and system status to the International Monitoring System (IMS), which forwards it via email to all subscribers. Vision provides tools for viewing and analyzing these stations’ state of health data.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2015

NASA's Nuclear Thermal Propulsion Project

Space fission power systems can provide a power rich environment anywhere in the solar system, independent of available sunlight. Space fission propulsion offers the potential for enabling rapid, affordable access to any point in the solar system. One type of space fission propulsion is Nuclear Thermal Propulsion (NTP). NTP systems operate by using a fission reactor to heat hydrogen to very high temperature (>2500 K) and expanding the hot hydrogen through a supersonic nozzle. First generation NTP systems are designed to have an Isp of approximately 900 s. The high Isp of NTP enables rapid crew transfer to destinations such as Mars, and can also help reduce mission cost, improve logistics (fewer launches), and provide other benefits. However, for NTP systems to be utilized they must be affordable and viable to develop. NASA's Advanced Exploration Systems (AES) NTP project is a technology development project that will help assess the affordability and viability of NTP. Early work has included fabrication of representative graphite composite fuel element segments, coating of representative graphite composite fuel element segments, fabrication of representative cermet fuel element segments, and testing of fuel element segments in the Compact Fuel Element Environmental Tester (CFEET). Near-term activities will include testing approximately 16" fuel element segments in the Nuclear Thermal Rocket Element Environmental Simulator (NTREES), and ongoing research into improving fuel microstructure and coatings. In addition to recapturing fuels technology, affordable development, qualification, and utilization strategies must be devised. Options such as using low-enriched uranium (LEU) instead of highly-enriched uranium (HEU) are being assessed, although that option requires development of a key technology before it can be applied to NTP in the thrust range of interest. Ground test facilities will be required, especially if NTP is to be used in conjunction with high value or crewed missions. There are potential options for either modifying existing facilities or constructing new ground test facilities. At least three potential options exist for reducing (or eliminating) the release of radioactivity into the environment during ground testing. These include fully containing the NTP exhaust during the ground test, scrubbing the exhaust, or utilizing an existing borehole at the Nevada National Security Site (NNSS) to filter the exhaust. Finally, the project is considering the potential for an early flight demonstration of an engine very similar to one that could be used to support human Mars or other ambitious missions. The flight demonstration could be an important step towards the eventual utilization of NTP.

Houts, Michael↗

DOE OSTI2024

A Study of the Transition to Turbulence in a Bed of 67 Spherical Pebbles

Packed beds are commonly found in many engineering systems and have been widely studied for decades. A relatively new packed bed system is the Pebble Bed Reactor, a type of generation-IV nuclear reactor. Unlike many of the packed beds encountered in chemical and process engineering applications, Pebble Bed Reactors are larger and operate at significantly higher Reynolds numbers. As a result of these differences, there is a very limited amount of information on the detailed flow physics that exist in these complex geometries. This work seeks to contribute to a growing database of flow data for Pebble Bed Reactor systems by performing Direct Numerical Simulations of the flow in an experimental bed of 67 pebbles for a range of conditions. Simulations are performed at a Prandtl number of 0.66 and Reynolds numbers from 300–600. These Reynolds numbers are chosen to gain additional knowledge on the spatial development of turbulence in these systems. Analysis of the Turbulent Kinetic Energy, turbulence anisotropy, and Turbulent Heat Flux is performed. Results demonstrate significant development of the TKE across the tested range of Reynolds numbers. Examination of both the TKE and THF reveal that development first occurs near the center of the bed and propagates radially as the flow moves further into the bed. Notable regions of negative production of turbulent kinetic energy are observed in regions where flow accelerates around pebble contact points. Furthermore, these regions are found to coincide with regions of 1-component turbulence.Kindly check and confirm, all authors email id is correctly identified.These are correct

Direct numberical simulation↗