Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “3D temperature modeling”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 505 records · Page 28

3D TRISO particle-explicit compact meshing

The TRI-structural ISOtropic (TRISO) layered fuel particle is a robust nuclear fuel form offering enhanced safety and performance for advanced reactor concepts, including high-temperature gas-cooled reactors and other Generation IV designs. These poppy-seed-sized particles are embedded in a graphite matrix to form fuel elements that must withstand elevated temperatures and high burn-up levels. The heterogeneous nature of these fuel elements — comprising thousands of randomly distributed TRISO particles — produces complex stress fields and thermal gradients that one- and two-dimensional models cannot accurately capture. While three-dimensional modeling has improved predictions of dimensional changes, internal pressure buildup, and fission product transport under irradiation, current approaches rely on homogenized material properties that are known to have considerable divergence from experimental observations. This work presents a methodology for optimized random packing of TRISO fuel compacts and full three-dimensional mesh generation within the BISON fuel performance code, with each particle coating layer individually discretized. The resulting mesh was demonstrated through heat conduction simulations under representative in-reactor operating conditions, showing strong agreement with expected behavior. This capability enables detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating layer failures — all of which directly govern fuel performance and safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A hybrid machine-learning approach for analysis of methane hydrate formation dynamics in porous media with synchrotron CT imaging

Fast multi-phase processes in methane hydrate bearing samples pose a challenge for quantitative micro-computed tomography study and experiment steering due to complex tomographic data analysis involving time-consuming segmentation procedures. This is because of the sample's multi-scale structure, which changes over time, low contrast between solid and fluid materials, and the large amount of data acquired during dynamic processes. Here, a hybrid approach is proposed for the automatic segmentation of tomographic data from time-resolved imaging of methane gas-hydrate formation in sandy granular media, which includes a deep-learning 3D U-Net model. To prepare a training dataset for the 3D U-Net, a technique to automate data labeling based on sample-specific information about the mineral matrix immobility and occasional fluid movement in pores is proposed. Automatic segmentation allowed for studying properties of the hydrate growth in pores, as well as dynamic processes such as incremental flow and redistribution of pore brine. Results of the quantitative analysis showed that for typical gas-hydrate stability parameters (100 bar methane pressure, 7°C temperature) the rate of formation is slow (less than 1% per hour), after which the surface area of contact between brine and gas increases, resulting in faster formation (2.5% per hour). Hydrate growth reaches the saturation point after 11 h of the experiment. Finally, the efficacy of the proposed segmentation scheme in on-the-fly automatic data analysis and experiment steering with zooming to regions of interest is demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Challenges in Laser Sintering of Melt-Processable Thermoset Imide Resin

Polymer Laser Sintering (LS) is an additive manufacturing technique that builds 3D models layer by layer using a laser to selectively melt cross sections in powdered polymeric materials, following sequential slices of the CAD model. LS generally uses thermoplastic polymeric powders, such as polyamides (i.e. Nylon), and the resultant 3D objects are often weaker in their strength compared to traditionally processed materials, due to the lack of polymer inter-chain connection in the z-direction. The objective of this project is to investigate the possibility of printing a melt-processable RTM370 imide resin powder terminated with reactive phenylethynyl groups by LS, followed by a postcure in order to promote additional crosslinking to achieve higher temperature (250-300 C) capability. A preliminary study to build tensile specimens by LS and the corresponding DSC and rheology study of RTM370 during LS process is presented.

Additive Manufacturing↗

Challenges in Laser Sintering of Thermoset Imide Resin

Polymer Laser Sintering (LS) is an additive manufacturing technique that builds 3D models layer by layer using a laser to selectively melt cross sections in powdered polymeric materials, following sequential slices of the CAD model. LS generally uses thermoplastic polymeric powders, such as polyamides (i.e. Nylon), and the resultant 3D objects are often weaker in their strength compared to traditionally processed materials, due to the lack of polymer inter-chain connection in the z-direction. The objective of this project is to investigate the possibility of printing a melt-processable RTM370 imide resin powder terminated with reactive phenylethynyl groups by LS, followed by a postcure in order to promote additional crosslinking to achieve higher temperature (250-300 C) capability. A preliminary study to build tensile specimens by LS and the corresponding DSC and rheology study of RTM370 during LS process is presented.

Additive Manufacturing↗

Evaluation of Mechanistic and Empirical Models against Existing FFRD and LOCA Experimental Databases

The desire of the nuclear industry to improve the economics of existing nuclear power plants has necessitated research into the potential of a phenomenon known as fuel fragmentation, relocation, and dispersal (FFRD). This phenomenon is possible during a loss-of-coolant accident (LOCA) at relatively high burnup. The Nuclear Energy Advanced Modeling and Simulation program has been developing simulation capabilities for FFRD and LOCA in the BISON fuel performance code for multiple years. This year, the effort has been focused on evaluating new lower length scale informed pulverization thresholds as well as updating and adding new empirical models for various phenomena. Models added or updated this year include a preliminary transient fission gas release model, new high-temperature Zircaloy creep models, a Zircaloy rupture opening area model, and a temperature-dependent emissivity during radiation from the fuel rod to the surrounding atmosphere. The models are verified through implementation tests to demonstrate code correctness after addition to BISON. The models are then assessed against a subset of the existing BISON validation suite for LOCA and FFRD cases. Two new cases, Studsvik Rods 192 and 193, have been added. The results indicate that the inclusion of a bubble pressure evolution model in the bubbles in the high-burnup structure has the largest impact compared to the 3D fracture criterion on reducing the calculated amount of pulverized fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Sensitivity study of coupled chemical-CFD simulations for analyzing aluminum-clad spent nuclear fuel storage in sealed canisters

We report the United States Department of Energy (DOE) manages over 50 Metric Tons Heavy Metal (MTHM) of aluminum-clad spent nuclear fuel. One main source for DOE’s Aluminum-clad spent nuclear fuel (ASNF) inventory is the advanced test reactor (ATR) at the INL site, which makes this fuel of particular interest for storage scenarios. Road-ready and final disposition packaging configurations for the ATR fuel dictates storage within helium-backfilled, sealed DOE standard canisters. The conditions within these sealed canisters for extended (greater than50 year dry) storage is of interest. To further this goal, a three-dimensional (3D) multi-physics computational fluid dynamics (CFD) model is developed of the sealed DOE standard canisters. This 3D CFD model is one-way coupled with bulk gas radiolysis reactions considering sealed canisters with inert gas and possible trace amounts of air and water vapor. This study looks at the evolution of the thermal history of the canisters over a 50 year time period with a coupling to the chemical reactions occurring from radiolytic breakdown of residual water. A sensitivity study is then carried out over the parameters of the model including the fuel decay heat, residual water content, sealed pressure, canister external temperature, and canister emissivity. In pure helium, hydrogen generation rates are low, under 10 ppm, but hydrogen generation rates are affected greatly by the presence of even 1% residual air, increasing by 50-plus-fold, and nitric acid generation with residual air also occurs ranging from 500 to 4000 ppm after 50 years. The fuel decay heat and the residual water content show the most importance in the generation of hydrogen gas in pure air, and for nitric acid with a residual air condition. External temperature, canister emissivity and sealed pressure all show minor sensitivity effects to the generation of potentially harmful species.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Rashba exciton in a 2D perovskite quantum dot

The Rashba effect has been proposed to give rise to a bright exciton ground state in halide perovskite nanocrystals (NCs), resulting in very fast radiative recombination at room temperature and extremely fast radiative recombination at low temperature. In this paper we find the dispersion of the “Rashba exciton”, i.e., the exciton whose bulk dispersion reflects large spin–orbit Rashba terms in the conduction and valence bands and thus has minima at non-zero quasi-momenta. Placing Rashba excitonsin quasi-2D cylindrical quantum dots, we calculate size-dependent levels of confined excitons and their oscillator transition strengths. Here, we consider the implications of this model for two-dimensional hybrid organic–inorganic perovskites, discuss generalizations of this model to 3D NCs, and establish criteria under which a bright ground exciton state could be realized.

36 MATERIALS SCIENCE↗

NASA Tech Briefs, March 2009

Topics covered include: Improved Instrument for Detecting Water and Ice in Soil; Real-Time Detection of Dust Devils from Pressure Readings; Determining Surface Roughness in Urban Areas Using Lidar Data; DSN Data Visualization Suite; Hamming and Accumulator Codes Concatenated with MPSK or QAM; Wide-Angle-Scanning Reflectarray Antennas Actuated by MEMS; Biasable Subharmonic Membrane Mixer for 520 to 600 GHz; Hardware Implementation of Serially Concatenated PPM Decoder; Symbolic Processing Combined with Model-Based Reasoning; Presentation Extensions of the SOAP; Spreadsheets for Analyzing and Optimizing Space Missions; Processing Ocean Images to Detect Large Drift Nets; Alternative Packaging for Back-Illuminated Imagers; Diamond Machining of an Off-Axis Biconic Aspherical Mirror; Laser Ablation Increases PEM/Catalyst Interfacial Area; Damage Detection and Self-Repair in Inflatable/Deployable Structures; Polyimide/Glass Composite High-Temperature Insulation; Nanocomposite Strain Gauges Having Small TCRs; Quick-Connect Windowed Non-Stick Penetrator Tips for Rapid Sampling; Modeling Unsteady Cavitation and Dynamic Loads in Turbopumps; Continuous-Flow System Produces Medical-Grade Water; Discrimination of Spore-Forming Bacilli Using spoIVA; nBn Infrared Detector Containing Graded Absorption Layer; Atomic References for Measuring Small Accelerations; Ultra-Broad-Band Optical Parametric Amplifier or Oscillator; Particle-Image Velocimeter Having Large Depth of Field; Enhancing SERS by Means of Supramolecular Charge Transfer; Improving 3D Wavelet-Based Compression of Hyperspectral Images; Improved Signal Chains for Readout of CMOS Imagers; SOI CMOS Imager with Suppression of Cross-Talk; Error-Rate Bounds for Coded PPM on a Poisson Channel; Biomorphic Multi-Agent Architecture for Persistent Computing; and Using Covariance Analysis to Assess Pointing Performance.

Source record↗

Laser Sintering of Thermoset Polyimide Composites

Selective Laser Sintering (SLS) is an additive manufacturing technique that builds 3D models layer by layer using a laser to selectively melt cross sections in powdered polymeric materials, following sequential slices of the CAD model. SLS generally uses thermoplastic polymeric powders, such as polyamides (i.e. Nylon), and the resultant 3D objects are often weaker in their strength compared to traditionally processed materials, due to the lack of polymer inter-chain connection in the z-direction. Our previous effort showed the challenges of printing a melt-processable RTM370 imide resin powder terminated with reactive 4-phenylethynylphthalic anhydride by LS, due to its inherently low viscosity of these oligomers. This paper presented the first successful 3D printing of high temperature carbon fiber filled thermoset polyimide composites, followed by post cure cycles to promote additional crosslinking for achieving higher temperature (Tg = 370 °C) capability. The processes to build tensile specimens and a component by LS, and the characterization of RTM370 imide resin by DSC and rheology as well as evaluation of the LS printed polyimide composite specimens by SEM and mechanical tests will be discussed.

Polyimide Composites↗

Thermal Conductivity of 3D Woven Composite Thermal Protection System Materials via Multiscale Recursive Micromechanics

Multiscale micromechanics predictions have been made for the effective thermal conductivities and local thermal fields for a novel 3D woven composite thermal protection system material. The Multiscale Recursive Micromechanics approach, which enables micromechanics models to call other micromechanics models (or themselves recursively) to consider finer and finer length scales, has been employed. The multiscale model uses a recently developed version of the High-Fidelity Generalized Method of Cells micromechanics theory at each of three length scales. Results focus on the impact of the microstructural geometry representation at each length scale on the material’s effective thermal conductivity, along with the local thermal flux and temperature fields induced in the microstructures.

Composites↗

Thermal Conductivity of 3D Woven Composite Thermal Protection System Materials via Multiscale Recursive Micromechanics

Multiscale micromechanics predictions have been made for the effective thermal conductivities and local thermal fields for a novel 3D woven composite thermal protection system material. The Multiscale Recursive Micromechanics approach, which enables micromechanics models to call other micromechanics models (or themselves recursively) to consider finer and finer length scales, has been employed. The multiscale model uses a recently developed version of the High-Fidelity Generalized Method of Cells micromechanics theory at each of three length scales. Results focus on the impact of the microstructural geometry representation at each length scale on the material’s effective thermal conductivity, along with the local thermal flux and temperature fields induced in the microstructures.

composite↗

Uniaxial Tensile Properties of AS4 3D Woven Composites with Four Different Resin Systems: Experimental Results & Analysis - Property Computations

As a part of the NASA Composite Technology for Exploration project, eight different AS4 3D orthogonal woven composite panels were manufactured and were subjected to mechanical testing including uniaxial tension along the weaves' warp direction. Each set, with four different resin systems (KCR-IR6070, EP2400, RTM6, and RS-50), included weave architectures designed using 12K and 6K AS4 carbon fiber yarns. For the tension testing conducted at Room Temperature Ambient (RTA) conditions, the elastic modulus and strength of these eight panels (as-processed and thermally cycled) were measured and compared while the potential evolution of micro-cracking before and after thermal cycling were monitored via optical microscopy and X-Ray Computed Tomography. The data set also included test results of the as-processed materials at Elevated Temperature Wet (ETW) conditions. In the second part of this study, efforts were made to compute elastic constants for AS4 6K/RTM6 and AS4 12K/RTM6 materials by implementing a finite element approach and the Multiscale Generalized Method of Cells (MSGMC) technique developed at NASA Glenn Research Center. Digimat-FE was used to model the weave architectures, assign properties, calculate yarn properties, create the finite element mesh, and compute the elastic properties by applying periodic boundary conditions to finite element models of each repeating unit cell. The required input data for MSGMC was generated using Matlab® from Digimat exported weave information. Experimental and computational results were compared, and the differences and limitations in correlating to the test data were briefly discussed.

Property Computations↗

Uniaxial Tensile Properties of AS4 3D Woven Composites with Four Different Resin Systems: Experimental Results and Analysis: Property Computations

As a part of the NASA Composite Technology for Exploration project, eight different AS4 3D orthogonal woven composite panels were manufactured and were subjected to mechanical testing including uniaxial tension along the weaves' warp direction. Each set, with four different resin systems (KCR-IR6070, EP2400, RTM6, and RS-50), included weave architectures designed using 12K and 6K AS4 carbon fiber yarns. For the tension testing conducted at Room Temperature Ambient (RTA) conditions, the elastic modulus and strength of these eight panels (as-processed and thermally-cycled) were measured and compared while the potential evolution of micro-cracking before and after thermal cycling were monitored via optical microscopy and X-Ray Computed Tomography. The data set also included test results of the as-processed materials at Elevated Temperature Wet (ETW) conditions. In the second part of this study, efforts were made to compute elastic constants for AS4 6K/RTM6 and AS4 12K/RTM6 materials by implementing a finite element approach and the Multiscale Generalized Method of Cells (MSGMC) technique developed at NASA Glenn Research Center. Digimat-FE was used to model the weave architectures, assign properties, calculate yarn properties, create the finite element mesh, and compute the elastic properties by applying periodic boundary conditions to finite element models of each repeating unit cell. The required input data for MSGMC was generated using Matlab® from Digimat exported weave information. Experimental and computational results were compared, and the differences and limitations in correlating to the test data were briefly discussed.

Property Computations↗

Plasma Wall Interaction with 3-D Plasma Boundaries

The interaction of the edge plasma and the material surfaces is one of the most critical challenges on the path to harness fusion power as new, fundamental energy source. This challenge typically combines the thrust to reach high density, low temperature (detached) plasmas in front of the divertor target plates as well as understanding the plasma material interaction (PMI) in particular in this regime. The combination of both research thrusts represents an extraordinarily challenging subject encompassing spatial scales spanning nanometers to meters in all states of matter and across a broad energy range. Modeling capabilities, which help to interpret data from nowadays experiments and enable extrapolation to future devices are urgently required. This is in particular true for toroidal magnetic confinement devices with three-dimensional (3D) plasma boundaries. Such plasma boundary geometries occur in tokamaks, when small amplitude magnetic perturbations are used to stabilize the unruly edge plasma or in stellarators, that are inherently 3D plasma confinement devices. In this project, the impact of 3D plasma boundaries on the plasma material interaction (PMI) was assessed. This work focused on plasma boundary conditions, in which high-density conditions at the material surfaces yield mitigation of the otherwise immense heat and particle loads that these materials would see. These so-called high recycling and eventually detached plasma regimes are of great interest for future reactor operation. In the project, key features that are unique to 3D boundaries were explored in comparison to canonically assumed axisymmetric plasma edge situations in tokamaks. In particular, the relevance of the 3D boundary situation in the extrapolation to the plasma boundary solution at ITER, the next step fusion energy experiment under construction as a multi-national, world-wide large-science experiment in southern France, has been explored. The EMC3-EIRENE plasma edge fluid and kinetic neutral transport code has been advanced to cope with the challenging and unprecedented conditions in the ITER boundary plasma including 3D fields that are planned to be used to suppress harmful edge instabilities, the so-called edge localized modes. This is a vital integration challenge for ITER and the results from this grant have provide a leading capability for this assessment. It was shown that the detachment process in a 3D edge solution for ITER follows the recycling regimes that are known from axisymmetric solutions, but that multiple plasma exhaust channels connected to the material surfaces are established which feature individual recycling characteristics. Because these channels touch the material surfaces in the divertor in a 3D geometry, the compatibility with the plasma material interaction (PMI), including erosion and impurity generation has been found to be an important part of the integration challenge. To address this, the fully 3D plasma material interaction code ERO2 has been adapted to these ITER specific geometries and a homogeneous mixing model was implemented, that allows to consider the mixing of Be and Was used at ITER in the PMI modeling. This model enhancement has been used to study non-local migration of Be in the JET ITER like wall configuration and it has been shown that with this model such complex migration processes in ITER relevant plasma shapes and with ITER relevant plasma boundary conditions can be addressed. The combined modeling approach using EMC3-EIRENE as a plasma boundary transport code and the ERO2 specialized PMI model will be an asset for the continued preparations of ITER operation as well as for Fusion Pilot Plant efforts that have emerged in the U.S. during the evolution of this grant. The predictive capability of this numerical tool has been validated at the DIII-D US national fusion facility. Here, dedicated plasma edge diagnostics were implemented to measure the impurity household around a 3D edge plasma during ELM suppression by 3D fields. Dedicated experiments with local material probes using these diagnostics and the state-of-the-art suite of boundary measurements at DIII-D have shown that the 3D perturbation of the plasma edge that is excreted by such 3D control fields yield a perturbation of the plasma boundary flux structure and hence also of the resulting PMI. The 3D boundary plasma is composed out of helical magnetic flux channels that intersect the divertor targets at an angle relative to the main guiding field, i.e., the toroidal magnetic field component of the tokamak. A similar effect has been measured as well on limiter surfaces during the startup campaign at the new stellarator experiment Wendelstein 7-X. These experiments ad initial analysis with the ERO plasma material interaction model, suggested that the place of erosion for a given particle from the surface and its re-deposition can be different in such 3D field geometries yielding potentially a significant level of net-erosion. This is not the case for axisymmetric solutions, where it was shown in the past that the eroded particles are effectively re-deposited into gaps produced by erosion at the same position and hence the net-erosion levels are small. For ITER, the quest to suppress the ELMs and at the same time maintain the integrity of the divertor is an issue, which these fundamental findings will help to resolve. The coupling of this work to the extrapolation in the ITER program has been addressed by both the PI and the lead numerical scientist being ITER Science Fellows in the duration of the contract and forward. A second focus in the exploration of 3D boundary effects on tokamaks and stellarators has been set on the measurement of helium exhaust features with such 3D fields. This is important because He represents the ash of the fusion process and needs to be exhausted. It was shown that 3D field application compatible with suppression of ELMs yields an increase of the helium exhaust performance. The ratio of the effective helium confinement time over the energy confinement time was reduced by almost 50% which demonstrated that the impact of helium accumulation in the plasma core with respect to the confinement of energy to sustain the fusion reaction is significantly improved with such 3D control fields. It was shown that this is the case for tokamaks as well as stellarators. At the Large helical Device in Japan, a similar enhancement of the helium exhaust features when small amplitude additional 3D fields were applied was measured. This is an important additional function of 3D field application and its impact on ITER is presently being studied in combination with investigations of helium exhaust in 3D field geometries of stellarator devices.

3D plasma edge transport↗

Rectenna thermal model development

Deploying rectennas in space requires adapting existing designs developed for terrestrial applications to the space environment. One of the major issues in doing so is to understand the thermal performance of existing designs in the space environment. Toward that end, a 3D rectenna thermal model has been developed, which involves analyzing shorted rectenna elements and finite size rectenna element arrays. A shorted rectenna element is a single element whose ends are connected together by a material of negligible thermal resistance. A shorted element is a good approximation to a central element of a large array. This model has been applied to Brown's 2.45 GHz rectenna design. Results indicate that Brown's rectenna requires redesign or some means of enhancing the heat dissipation in order for the diode temperature to be maintained below 200 C above an output power density of 620 W/sq.m. The model developed in this paper is very general and can be used for the analysis and design of any type of rectenna design of any frequency.

Kadiramangalam, Murall↗

Levitation Technology in International Space Station Research

The International Space Station (ISS) is a unique multidisciplinary orbiting laboratory for science and technology research, enabling discoveries that benefit life on Earth and exploration of the universe. ISS facilities for containerless sample processing in Materials Science experiments include levitation devices with specimen positioning control while reducing containment vessel contamination. For example, ESA's EML (ElectroMagnetic Levitator), is used for melting and solidification of conductive metals, alloys, or semiconductors in ultra-high vacuum, or in high-purity gaseous atmospheres. Sample heating and positioning are accomplished through electromagnetic fields generated by a coil system. EML applications cover investigation of solidification and microstructural formation, evaluation of thermophysical properties of highly reactive metals (whose properties can be very sensitive to contamination), and examination of undercooled liquid metals to understand metastable phase convection and influence convection on structural changes. MSL utilization includes development of novel light-weight, high-performance materials. Another facility, JAXA's ELF (Electrostatic Levitation Furnace), is used to perform high temperature melting while avoiding chemical reactions with crucibles by levitating a sample through Coulomb force. ELF is capable of measuring density, surface tension, and viscosity of samples at high temperatures. One of the initial ELF investigations, Interfacial Energy-1, is aimed at clarification of interfacial phenomena between molten steels and oxide melts with industrial applications in control processes for liquid mixing. In addition to these Materials Science facilities, other ISS investigations that involve levitation employ it for biological research. For example, NASA's "Magnetic 3D Culturing and Bioprinting" investigation uses magnetic levitation for three-dimensional culturing and positioning of magnetized cells to generate spheroid assemblies for biomedical applications. Levitation is also used as a modeled microgravity ground analog in the NASA OsteoOmics ISS investigation, which tests whether magnetic levitation accurately simulates microgravity conditions by studying gravitational regulation of osteoblast and osteoclast genomics and metabolism. Elucidating the cellular mechanisms of bone loss in microgravity contributes to the understanding of bone loss in medical disorders on Earth, which may lead to development of preventive or therapeutic countermeasures. Thus, the ISS state-of-the-art laboratory offers various levitation capability platforms with applications for innovative research in Materials and Life Sciences disciplines, with benefits for humanity.

Guinart-Ramirez, Y.↗

The Impact of Firn Models on Ultrawideband Brightness Temperatures in the Partially Coherent Model

The density profile of a polar ice sheet is an important parameter for the estimation of ice mass balance. Wave reflections caused by density variations are also a key uncertainty in the retrieval of ice sheet temperature profiles in Ultra-Wide band radiometry. In this paper, we examine different firn density profile models and analyze the subsurface reflections they cause using an analytical partially coherent approach. We also examine firn density profiles obtained from borehole measurements, from past UWBRAD modeling studies, from a community firn model, and from snow radar echo measurements. In previous studies, the ice sheet has been model as a 1D random medium with density variations in depth. However, horizontal density variations also exist, so that the ice sheet is a 3D random medium. Analyses using the partially coherent model show that in the presence of horizontal fluctuations, contributions from short scale variations vanish as the horizontal correlation length decreases due to the diffraction of waves.

Haokui Xu↗