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NASA NTRS2010

Validation of a Three-Dimensional Ablation and Thermal Response Simulation Code

The 3dFIAT code simulates pyrolysis, ablation, and shape change of thermal protection materials and systems in three dimensions. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid system to simulate the shape change due to surface recession. This work is the first part of a code validation study for new capabilities that were added to 3dFIAT. These expanded capabilities include a multi-block moving grid system and an orthotropic thermal conductivity model. This paper focuses on conditions with minimal shape change in which the fluid/solid coupling is not necessary. Two groups of test cases of 3dFIAT analyses of Phenolic Impregnated Carbon Ablator in an arc-jet are presented. In the first group, axisymmetric iso-q shaped models are studied to check the accuracy of three-dimensional multi-block grid system. In the second group, similar models with various through-the-thickness conductivity directions are examined. In this group, the material thermal response is three-dimensional, because of the carbon fiber orientation. Predictions from 3dFIAT are presented and compared with arcjet test data. The 3dFIAT predictions agree very well with thermocouple data for both groups of test cases.

Chen, Yih-Kanq↗

NASA NTRS2015

Improved Rainfall Estimates and Predictions for 21st Century Drought Early Warning

As temperatures increase, the onset and severity of droughts is likely to become more intense. Improved tools for understanding, monitoring and predicting droughts will be a key component of 21st century climate adaption. The best drought monitoring systems will bring together accurate precipitation estimates with skillful climate and weather forecasts. Such systems combine the predictive power inherent in the current land surface state with the predictive power inherent in low frequency ocean-atmosphere dynamics. To this end, researchers at the Climate Hazards Group (CHG), in collaboration with partners at the USGS and NASA, have developed i) a long (1981-present) quasi-global (50degS-50degN, 180degW-180degE) high resolution (0.05deg) homogenous precipitation data set designed specifically for drought monitoring, ii) tools for understanding and predicting East African boreal spring droughts, and iii) an integrated land surface modeling (LSM) system that combines rainfall observations and predictions to provide effective drought early warning. This talk briefly describes these three components. Component 1: CHIRPS The Climate Hazards group InfraRed Precipitation with Stations (CHIRPS), blends station data with geostationary satellite observations to provide global near real time daily, pentadal and monthly precipitation estimates. We describe the CHIRPS algorithm and compare CHIRPS and other estimates to validation data. The CHIRPS is shown to have high correlation, low systematic errors (bias) and low mean absolute errors. Component 2: Hybrid statistical-dynamic forecast strategies East African droughts have increased in frequency, but become more predictable as Indo- Pacific SST gradients and Walker circulation disruptions intensify. We describe hybrid statistical-dynamic forecast strategies that are far superior to the raw output of coupled forecast models. These forecasts can be translated into probabilities that can be used to generate bootstrapped ensembles describing future climate conditions. Component 3: Assimilation using LSMs CHIRPS rainfall observations (component 1) and bootstrapped forecast ensembles (component 2) can be combined using LSMs to predict soil moisture deficits. We evaluate the skill such a system in East Africa, and demonstrate results for 2013.

Funk, Chris↗

NASA NTRS2015

Improved Rainfall Estimates and Predictions for 21st Century Drought Early Warning

Funk, Chris↗

NASA NTRS2007

Quasi-Periodic Variability in NGC 5408 X-1

We report the discovery with XMM-Newton of quasiperiodic variability in the 0.2 - 10 keV X-ray flux from the ultraluminous X-ray source NGC 5408 X-1. The average power spectrum of all EPIC-pn data reveals a strong 20 mHz QPO with an average amplitude (rms) of 9%, and a coherence, Q identical with nu(sub 0)/sigma approximately equal to 6. In a 33 ksec time interval when the 20 mHz QPO is strongest we also find evidence for a 2nd QPO peak at 15 mHz, the first indication for a close pair of QPOs in a ULX source. Interestingly, the frequency ratio of this QPO pair is inconsistent with 3:2 at the 3 sigma level, but is consistent with a 4:3 ratio. A powerlaw noise component with slope near 1.5 is also present below 0.1 Hz with evidence for a break to a flatter slope at about 3 mHz. The source shows substantial broadband variability, with a total amplitude (rms) of about 30% in the 0.1 - 100 mHz frequency band, and there is strong energy dependence to the variability. The power spectrum of hard X-ray photons (greater than 2 keV) shows a "classic" flat-topped continuum breaking to a power law with index 1.5 - 2. Both the break and 20 mHz QPO are detected in the hard band, and the 20 mHz QPO is essentially at the break. The QPO is both strong and narrow in this band, having an amplitude (rms) of 15%, and Q approx. equal to 25. The energy spectrum is well fit by three components, a "cool" disk with kT = 0.15 keV, a steep power law with index 2.56, and a thermal plasma at kT = 0.87 keV. The disk, power law, and thermal plasma components contribute 35, 60, and 5% of the 0.3 - 10 keV flux, respectively. Both the timing and spectral properties of NGC 5408 X-1 are strikingly reminiscent of Galactic black hole systems at high inferred accretion rates, but with its characteristic frequencies (QPO and break frequencies) scaled down by a factor of 10 - 100. We discuss the implications of these findings in the context of models for ULXs, and their implications for the object's mass.

Strohmayer, Tod E.↗

NASA NTRS2004

Improved Refractometer for Measuring Temperatures of Drops

The Dual Rainbow refractometer is an enhanced version of the Rainbow refractometer, which is added to, and extends the capabilities of, a phase Doppler particle analyzer (PDPA). A PDPA utilizes pairs of laser beams to measure individual components of velocity and sizes of drops in a spray. The Rainbow-refractometer addition measures the temperatures of individual drops. The designs of prior versions of the Rainbow refractometer have required substantial modifications of PDPA transmitting optics, plus dedicated lasers as sources of illumination separate from, and in addition to, those needed for PDPA measurements. The enhancement embodied in the Dual Rainbow refractometer eliminates the need for a dedicated laser and confers other advantages as described below. A dedicated laser is no longer needed because the Dual Rainbow refractometer utilizes one of the pairs of laser beams already present in a PDPA. Hence, the design of the Dual Rainbow refractometer simplifies the task of upgrading PDPA hardware to enable measurement of temperature. Furthermore, in a PDPA/Dual Rainbow refractometer system, a single argon-ion laser with three main wavelengths can be used to measure the temperatures, sizes, and all three components of velocity (in contradistinction to only two components of velocity in a prior PDPA/Rainbow refractometer system). In order to enable the Dual Rainbow refractometer to utilize a pair of PDPA laser beams, it was necessary to (1) find a location for the refractometer receiver, such that the combined rainbow patterns of two laser beams amount to a pattern identical to that of a single beam, (2) adjust the polarization of the two beams to obtain the strongest rainbow pattern, and (3) find a location for the PDPA receiver to obtain a linear relationship between the measured phase shift and drop size.

Naqwi, Amir A.↗

NASA NTRS1997

Models of Speed Discrimination

The prime purpose of this project was to investigate various theoretical issues concerning the integration of information across visual space. To date, most of the research efforts in the study of the visual system seem to have been focused in two almost non-overlaping directions. One research focus has been the low level perception as studied by psychophysics. The other focus has been the study of high level vision exemplified by the study of object perception. Most of the effort in psychophysics has been devoted to the search for the fundamental "features" of perception. The general idea is that the most peripheral processes of the visual system decompose the input into features that are then used for classification and recognition. The experimental and theoretical focus has been on finding and describing these analyzers that decompose images into useful components. Various models are then compared to the physiological measurements performed on neurons in the sensory systems. In the study of higher level perception, the work has been focused on the representation of objects and on the connections between various physical effects and object perception. In this category we find the perception of 3D from a variety of physical measurements including motion, shading and other physical phenomena. With few exceptions, there seem to be very limited development of theories describing how the visual system might combine the output of the analyzers to form the representation of visual objects. Therefore, the processes underlying the integration of information over space represent critical aspects of vision system. The understanding of these processes will have implications on our expectations for the underlying physiological mechanisms, as well as for our models of the internal representation for visual percepts. In this project, we explored several mechanisms related to spatial summation, attention, and eye movements. The project comprised three components: 1. Modeling visual search for the detection of speed deviation. 2. Perception of moving objects. 3. Exploring the role of eye movements in various visual tasks.

Source record↗

DOE OSTI2023

Accelerating full-waveform inversion using source stacking: synthetic experiments at the global scale in a realistic 3-D earth model

SUMMARY The spectral element method is currently the method of choice for computing accurate synthetic seismic wavefields in realistic 3-D earth models at the global scale. However, it requires significantly more computational time, compared to normal mode-based approximate methods. Source stacking, whereby multiple earthquake sources are aligned on their origin time and simultaneously triggered, can reduce the computational costs by several orders of magnitude. We present the results of synthetic tests performed on a realistic radially anisotropic 3-D model, slightly modified from model SEMUCB-WM1 with three component synthetic waveform ‘data’ for a duration of 10 000 s, and filtered at periods longer than 60 s, for a set of 273 events and 515 stations. We consider two definitions of the misfit function, one based on the stacked records at individual stations and another based on station-pair cross-correlations of the stacked records. The inverse step is performed using a Gauss–Newton approach where the gradient and Hessian are computed using normal mode perturbation theory. We investigate the retrieval of radially anisotropic long wavelength structure in the upper mantle in the depth range 100–800 km, after fixing the crust and uppermost mantle structure constrained by fundamental mode Love and Rayleigh wave dispersion data. The results show good performance using both definitions of the misfit function, even in the presence of realistic noise, with degraded amplitudes of lateral variations in the anisotropic parameter ξ. Interestingly, we show that we can retrieve the long wavelength structure in the upper mantle, when considering one or the other of three portions of the cross-correlation time series, corresponding to where we expect the energy from surface wave overtone, fundamental mode or a mixture of the two to be dominant, respectively. We also considered the issue of missing data, by randomly removing a successively larger proportion of the available synthetic data. We replace the missing data by synthetics computed in the current 3-D model using normal mode perturbation theory. The inversion results degrade with the proportion of missing data, especially for ξ, and we find that a data availability of 45 per cent or more leads to acceptable results. We also present a strategy for grouping events and stations to minimize the number of missing data in each group. This leads to an increased number of computations but can be significantly more efficient than conventional single-event-at-a-time inversion. We apply the grouping strategy to a real picking scenario, and show promising resolution capability despite the use of fewer waveforms and uneven ray path distribution. Source stacking approach can be used to rapidly obtain a starting 3-D model for more conventional full-waveform inversion at higher resolution, and to investigate assumptions made in the inversion, such as trade-offs between isotropic, anisotropic or anelastic structure, different model parametrizations or how crustal structure is accounted for.

Geochemistry & Geophysics↗

DOE OSTI2023

Seismic Monitoring at the Farnsworth CO2-EOR Field Using Time-Lapse Elastic-Waveform Inversion of 3D-3C VSP Data

During the Development Phase of the U.S. Southwest Regional Partnership on Carbon Sequestration, supercritical CO2 was continuously injected into the deep oil-bearing Morrow B formation of the Farnsworth Unit in Texas for Enhanced Oil Recovery (EOR). The project injected approximately 94 kilotons of CO2 to study geologic carbon storage during CO2-EOR. A three-dimensional (3D) surface seismic dataset was acquired in 2013 to characterize the subsurface structures of the Farnsworth site. Following this data acquisition, the baseline and three time-lapse three-dimensional three-component (3D-3C) vertical seismic profiling (VSP) data were acquired at a narrower surface area surrounding the CO2 injection and oil/gas production wells between 2014 and 2017 for monitoring CO2 injection and migration. With these VSP datasets, we inverted for subsurface velocity models to quantitatively monitor the CO2 plume within the Morrow B formation. We first built 1D initial P-wave (Vp) and S-wave (Vs) velocity models by upscaling the sonic logs. We improved the deep region of the Vp and Vs models by incorporating the deep part of a migration velocity model derived from the 3D surface seismic data. We improved the shallow region of 3D Vp and Vs models using 3D traveltime tomography of first arrivals of VSP downgoing waves. We further improved the 3D baseline velocity models using elastic-waveform inversion (EWI) of the 3D baseline VSP upgoing data. Our advanced EWI method employs alternative tomographic and conventional gradients and total-variation-based regularization to ensure the high-fidelity updates of the 3D baseline Vp and Vs models. We then sequentially applied our 3D EWI method to the three time-lapse datasets to invert for spatiotemporal changes of Vp and Vs in the reservoir. Our inversion results reveal the volumetric changes of the time-lapse Vp and Vs models and show the evolution of the CO2 plume from the CO2 injection well to the oil/gas production wells.

42 ENGINEERING↗

NASA NTRS1993

Polytopic vector analysis in igneous petrology: Application to lunar petrogenesis

Lunar samples represent a heterogeneous assemblage of rocks with complex inter-relationships that are difficult to decipher using standard petrogenetic approaches. These inter-relationships reflect several distinct petrogenetic trends as well as thermomechanical mixing of distinct components. Additional complications arise from the unequal quality of chemical analyses and from the fact that many samples (e.g., breccia clasts) are too small to be representative of the system from which they derived. Polytopic vector analysis (PVA) is a multi-variate procedure used as a tool for exploratory data analysis. PVA allows the analyst to classify samples and clarifies relationships among heterogenous samples with complex petrogenetic histories. It differs from orthogonal factor analysis in that it uses non-orthogonal multivariate sample vectors to extract sample endmember compositions. The output from a Q-mode (sample based) factor analysis is the initial step in PVA. The Q-mode analysis, using criteria established by Miesch and Klovan and Miesch, is used to determine the number of endmembers in the data system. The second step involves determination of endmembers and mixing proportions with all output expressed in the same geochemical variable as the input. The composition of endmembers is derived by analysis of the variability of the data set. Endmembers need not be present in the data set, nor is it necessary for their composition to be known a priori. A set of any endmembers defines a 'polytope' or classification figure (triangle for a three component system, tetrahedron for a four component system, a 'five-tope' in four dimensions for five component system, et cetera).

Shervais, John W.↗

DOE OSTI2020

Using Low-Cost “Garage Band” Recording Technology for Acquiring High Resolution High-Speed Data

The Oak Ridge National Laboratory (ORNL) has developed and tested a novel system architecture for acquiring high fidelity high-speed data. The approach uses a consumer grade audio recording device that is normally associated with “garage band” recording of music. ORNL has coupled this low-cost data acquisition hardware with computing technology running open-source software. The main advantage of this approach is per-channel cost; an instrument grade data acquisition system typically costs between $800 to $2000 per channel compared to less than $50 per channel for these consumer grade components. Three systems, each featuring four channels, have been deployed for acquiring data from geophones and the electrical supply system that supports the High Flux Isotope Reactor (HFIR) and the Radiochemical Engineering Development Center (REDC) at ORNL. Each channel samples at 96 kHz at 24-bit resolution. The deployed systems operate continuously 24/7 and produce about 4 terabytes of data per month per system. This paper provides a technical overview of this approach, its implementation, and some preliminary results from qualification testing. This work was conducted in support of the Multi-Informatics for Nuclear Operations Scenarios (MINOS).Keywords: Data acquisition Measurement Informatics

Wetherington Jr, G↗

DOE OSTI2023

Toward an Autonomous Workflow for Single Crystal Neutron Diffraction

The operation of the neutron facility relies heavily on beamline scientists. Some experiments can take one or two days with experts making decisions along the way. Leveraging the computing power of HPC platforms and AI advances in image analyses, here we demonstrate an autonomous workflow for the single-crystal neutron diffraction experiments. The workflow consists of three components: an inference service that provides real-time AI segmentation on the image stream from the experiments conducted at the neutron facility, a continuous integration service that launches distributed training jobs on Summit to update the AI model on newly collected images, and a frontend web service to display the AI tagged images to the expert. Ultimately, the feedback can be directly fed to the equipment at the edge in deciding the next-step experiment without requiring an expert in the loop. With the analyses of the requirements and benchmarks of the performance for each component, this effort serves as the first step toward an autonomous workflow for real-time experiment steering at ORNL neutron facilities.

Yin, Junqi↗

DOE OSTI2026

Pulsed laser synthesis of mesoporous metal chalcogenide thin films

Mesoporous films of the metal chalcogenide B-FeSe were grown on MgO substrates by KrF pulsed laser deposition (PLD) in an argon background. At 100 mTorr, gated intensified charge-coupled device imaging and ion probe measurements showed that the plasma plume responsible for crystal growth initially comprised three components, with distinct expansion velocities. Plume interactions with the substrate heater and ablation target gave rise to complex dynamics, including collisions between the charged leading edge—rebounding between the substrate and the target—and slower-moving species in the plume interior. Film growth was dominated by species with kinetic energies ≤0.5 eV/atom. X-ray reflectivity revealed that films grown in this environment—with a substrate temperature of 350 ° C, a laser fluence of 1.0 J cm −2 , and a 7.5 mm 2 spot area—formed a porous framework with 15% porosity. Atomic force microscopy showed surface features that suggest pore sizes below 100 nm. X-ray diffraction indicated that the porous films were epitaxial with respect to the substrate and likely grew by oriented-attachment of gas-phase molecular clusters or very small nanoparticles, in contrast to the conventional epitaxy of vacuum films from atomic constituents. The in-plane orientation of the mesoporous films was B-FeSe [100]||[110] MgO, attributed to the soft landing of pre-formed crystallites on the MgO substrates, where protruding Se rows of B-FeSe aligned with corrugations of the MgO surface. In conclusion, this work implies that growth of candidate electrocatalyst materials by PLD in inert gas background may allow mesoporous frameworks with a single crystallographic orientation that expose specific crystal facets for electrochemical reactions and active site engineering.

cluster epitaxy↗

DOE OSTI2025

Second-generation downscaled earth system model data using generative machine learning

The second-generation Sup3rCC dataset provides high-resolution meteorological data generated through the downscaling of multiple earth system models (ESMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6). This downscaling is performed through application of a generative machine learning approach called Super-Resolution for Renewable Resource Data (sup3r). This dataset builds on the first-generation Sup3rCC data by applying improved bias correction methods and adding downscaled precipitation to the output variables. As with the first Sup3rCC version, the data still include temperature, wind speed and direction at multiple heights, pressure, three components of downwelling solar radiation, and relative humidity—all at 4-kilometer (km) hourly resolution over the contiguous United States. This is a 25x spatial enhancement and 24x temporal enhancement of the source 100-km daily-average ESM data. This extension of the Sup3rCC dataset includes data from six ESMs from two shared socioeconomic pathways (SSPs) totaling 400 years of data with multiple future projections of changing meteorological conditions. The scenario selection was based on a structured evaluation of historical ESM skill and comprehensive representation of possible trajectories of future climate change in temperature, humidity, precipitation, solar irradiance, and near-surface wind speeds. The inclusion of multiple future projections is intended to enable users to assess key drivers of un 36 certainty and variability. All data are double-bias corrected, resulting in a product that can be used out-of-the-box for energy system analysis with minimal historical bias. The potential applications of Sup3rCC data extend to various topics in renewable energy resource assessment, energy systems modeling, and grid resilience studies. High-resolution future meteorological projections are critical for evaluating the effects of changing meteorological conditions on renewable energy generation, energy demand, and for optimizing energy storage and grid infrastructure. The 4-km hourly resolution of the downscaled data enables understanding of spatial and temporal variability at the scales necessary for energy system operational planning. In addition, the dataset can support risk assessments by providing detailed information on possible future extreme weather events and long-term meteorological variability at scales relevant to energy infrastructure. By offering an enhanced representation of possible future meteorological conditions, the second-generation Sup3rCC dataset enables more precise modeling of energy resilience and adaptation strategies in response to changing meteorological conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Modeling strategy for progressive failure prediction in lithium-ion batteries under mechanical abuse

The prediction for the internal failure of lithium-ion batteries (LIBs) under external mechanical abuse loading remains a challenge for safe design. This paper systematically studies the modeling approach for progressive failure simulation and short-circuit prediction. Hemispherical indentation experiments are conducted on a battery specimen containing 5 representative sandwich (RS) layers to examine the deformation and progressive failure behavior of battery components. Three different models, viz, a high-fidelity detailed model, an intermediate homogenized model and a fully homogenized model, are developed and employed to simulate the progressive failure in a multi-layer battery specimen. The simulation results obtained using the three models all correlate well with experimental phenomena, capturing the overall stress-strain response and ultimate failure of the battery structure. The numerical results can help us understand the failure behavior and the mechanism for mechanical abuse-induced short circuit in LIBs. The feasibility of the three models for use in progressive failure prediction is compared by analyzing the capability of the models in predicting the critical failure events, the computational efficiency of the models, and the feasibility to implement coupled mechanical-electrochemical-thermal simulations. The results of this work provide useful insights on practical choices for the modeling strategy and safety design of LIBs under mechanical abuse conditions.

25 ENERGY STORAGE↗

DOE OSTI2020

Meso-scale modeling and damage analysis of carbon/epoxy woven fabric composite under in-plane tension and compression loadings

The mechanical properties and damage behaviors of carbon/epoxy woven fabric composite under in-plane tension and compression are studied at the meso-scale level through experiment and simulation. An efficient representative volume element (RVE) modeling method with consistent mesh, high yarn volume fraction and realistic geometry is proposed. The material constitutive laws with plasticity, tension-compression asymmetry and damage evolution are established for the three components - yarn, matrix and interface, respectively. Significantly different mechanical properties and damage evolutions are observed depending on loading conditions and initial geometry characteristics. It shows a non-linear stress-strain curve with clear transition region and intensive damage in tension, while a quasi-linear behavior up to facture is observed in compression with little damage prior to final fracture. Furthermore, compared to the constant Poisson's ratio with straining in compression, a dramatic increase in Poisson's ratio appears in tension. Simulation shows damage mechanisms including transverse damage, matrix damage and delamination, which all play critical roles in the property evolution. In particular, the rapid damage accumulation after elastic deformation destroys the strong bonds and causes the easy deformation of transverse yarns which results in the transition region and large Poisson's ratio in tension. All the mechanical behaviors and damage evolutions are well captured and explained with the current RVE model.

42 ENGINEERING↗

DOE OSTI2025

Speciation mapping of the oxidation layer on aged uranium dioxide using scanning transmission x-ray spectromicroscopy

In this study, UO 2 was aged in humid air and prepared as a thin section using a focused ion beam (FIB) instrument. The specimen was measured using synchrotron radiation spectromicroscopy techniques at the Beamline 11.0.2 STXM end station of the Advanced Light Source (ALS). Non-negative matrix factorization (NMF) methods were used to identify and map three component x-ray absorption near-edge structure (XANES) spectra in the oxygen K-edge data, revealing a surface layer of U 4 O 9 with a thickness of 206 ± 21 nm, and the bulk of the sample remaining as UO 2 . Uranium N 4,5 -edge XANES spectromicroscopy supports these results. The diffusion-controlled parabolic rate constant for UO 2 oxidation to U 4 O 9 was calculated from the observed layer thickness and compared to literature values. Complementary transmission electron microscopy (TEM) was used to image the sample and identify the phases present in various regions, confirming the STXM results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Enhanced performance of Bi 2 S 3 /TiO 2 heterostructure composite films for solar cell applications

Day to day energy production is shifting towards renewable energy sources as these sources become more economically viable while being less polluting to operate; solar energy has become one of the major sources of renewable energy. However, it currently relies on ultra-pure silicon ingots to produce commercial silicon photovoltaics, which prevents the cost of electricity being produced to compete with non-renewable energy production. A viable low-cost alternative for silicon based cells would be dye-sensitized solar cells (DSSCs), which are easier and cheaper to manufacture as they do not require expensive and delicate raw materials to make. Moreover, they could be made semi-flexible which allows for a greater variety of applications. A DSSC consists of three components, a photo-electrode, an electrolyte and a counter-electrode. When exposed to incident light, the complex photosensitizers in the photoelectrode release electrons which are transported to the external load, leaving the photoelectrode in an oxidized state. The electrons are collected by the counter electrode and used to reduce the electrolyte. This charged electrolyte then reduces the positively charged photoelectrode, allowing the process to begin again. To improve the efficiency of this process, we explore the use of bismuth sulfide (Bi 2 S 3 ) and titanium oxide (TiO 2 ) composite as photoelectrode material and investigate their impact on the efficiency of DSSC.

14 SOLAR ENERGY↗

DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗