Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “spectral prediction”

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 487 records · Page 27

A solar spectral line list between 10 and 200 A modified for application to high spectral resolution X-ray astronomy

A spectral line list for the 10-200 A range is developed from existing solar spectra for application to high spectral resolution measurements of astrophysical plasmas. The solar spectral line lists are merged into a single comprehensive list. The effect of the solar emission measure distribution is removed from the line intensities, which results in a set of emission rates for the lines that can be applied to many optically thin, low density high temperature plasmas in ionization equilibrium. In addition to the measured solar lines, 250 theoretical lines are added to this list. These lines fall in wavelength regions where the existing solar lists have few lines because of limitations in instrumental sensitivity. Also, some lines have been added because the sun has very little plasma at temperatures of about one million K, and consequently these lines are weak or absent in solar spectra. The entire list contains about 600 lines. Finally, predicted spectra of the two RS CVn stars, alpha Aur (Capella) and UX Ari, are presented at 1 and 0.25 A spectral resolution. Also, the solar spectrum is shown at 1 A resolution, and the emission rate spectrum (spectrum not modified by an emission measure distribution) is shown at very high spectral resolution. The predicted spectra for Capella and UX Ari are based on results obtained from the Einstein and International Ultraviolet Explorer (IUE) spacecraft.

Doschek, G. A.↗

Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers

A striking example of frustration in physics is Hofstadter’s butterfly, a fractal structure that emerges from the competition between a crystal’s lattice periodicity and the magnetic length of an applied field. Current methods for predicting the topological invariants associated with Hofstadter’s butterfly are challenging or impossible to apply to a range of materials, including those that are disordered or lack a bulk spectral gap. Here, in this work, we demonstrate a framework for predicting a material’s local Chern markers using its position-space description and validate it against experimental observations of quantum transport in artificial graphene in a semiconductor heterostructure, inherently accounting for fabrication disorder strong enough to close the bulk spectral gap. By resolving local changes in the system’s topology, we reveal the topological origins of antidot-localized states that appear in artificial graphene in the presence of a magnetic field. Moreover, we show the breadth of this framework by simulating how Hofstadter’s butterfly emerges from an initially unpatterned 2D electron gas as the system’s potential strength is increased and predict that artificial graphene becomes a topological insulator at the critical magnetic field. Overall, we anticipate that a position-space approach to determine a material’s Chern invariant without requiring prior knowledge of its occupied states or bulk spectral gaps will enable a broad array of fundamental inquiries and provide a novel route to material discovery, especially in metallic, aperiodic, and disordered systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

In Situ Prediction of Microstructure and Mechanical Properties in Laser-Remelted Al-Si Alloys: Towards Enhanced Additive Manufacturing

Laser surface remelting of aluminum alloys has emerged as a promising technique to enhance mechanical properties through refined microstructures. This process involves rapid cooling rates ranging from 10 3 to 10 8 °C/s, which increase solid solubility within aluminum alloys, shifting their eutectic composition to a larger value of silicon content. Consequently, the resulting microstructure combines a strengthened aluminum matrix with silicon fibers. This study focuses on the laser scanning of Al-Si aluminum alloy to reduce the size of aluminum matrix spacings and transform fibrous silicon particles from micrometer to nanometer dimensions. Analysis revealed that the eutectic structure contained 17.55% silicon by weight, surpassing the equilibrium eutectic composition of 12.6% silicon. Microstructure dimensions within the molten zones, termed ‘melt pools’, were extensively examined using Scanning Electron Microscopy (SEM) at intervals of approximately 20 μm from the surface. A notable increase in hardness, exceeding 50% compared to the base plate, was observed in the melt pool regions. Thus, it is exemplified that laser surface remelting introduces a novel strengthening mechanism in the alloy. Moreover, this study develops an in situ method for predicting melt pool properties and dimensions. A predictive model is proposed, correlating energy density and spectral signals emitted during laser remelting with mechanical properties and melt pool dimensions. This method significantly reduces characterization time from days to seconds, offering a streamlined approach for future studies in additive manufacturing.

36 MATERIALS SCIENCE↗

Radiometric Calibration of A Non-Imaging Airborne Spectrometer To Measure the Greenland Ice Sheet Surface

Methods to radiometrically calibrate a non-imaging airborne visible-to-shortwave infrared (VSWIR) spectrometer to measure the Greenland ice sheet surface are presented. Airborne VSWIR measurement performance for bright Greenland ice and dark bare rock/soil targets is compared against the MODerate resolution atmospheric TRANsmission (MODTRAN ® ) radiative transfer code (version 6.0), and a coincident Landsat 8 Operational Land Imager (OLI) acquisition on 29 July 2015 during an in-flight radiometric calibration experiment. Airborne remote sensing flights were carried out in northwestern Greenland in preparation for the Ice, Cloud, and land Elevation Satellite 2 (ICESat-2) laser altimeter mission. A total of nine science flights were conducted over the Greenland ice sheet, sea ice, and open-ocean water. The campaign's primary purpose was to correlate green laser pulse penetration into snow and ice with spectroscopic-derived surface properties. An experimental airborne instrument configuration that included a nadir-viewing (looking downward at the surface) non-imaging Analytical Spectral Devices (ASD) Inc. spectrometer that measured upwelling VSWIR (0.35 to 2.5 µm) spectral radiance (Wm −2 sr −1 µm −1 ) in the two-color Slope Imaging Multi-polarization Photon-Counting Lidar's (SIMPL) ground instantaneous field of view, and a zenith-viewing (looking upward at the sky) ASD spectrometer that measured VSWIR spectral irradiance (W m −2 nm −1 ) was flown. National Institute of Standards and Technology (NIST) traceable radiometric calibration procedures for laboratory, in-flight, and field environments are described in detail to achieve a targeted VSWIR measurement requirement of within 5 % to support calibration/validation efforts and remote sensing algorithm development. Our MODTRAN predictions for the 29 July flight line over dark and bright targets indicate that the airborne nadir-viewing spectrometer spectral radiance measurement uncertainty was between 0.6 % and 4.7 % for VSWIR wavelengths (0.4 to 2.0 µm) with atmospheric transmittance greater than 80 %. MODTRAN predictions for Landsat 8 OLI relative spectral response functions suggest that OLI is measuring 6 % to 16 % more top-of-atmosphere (TOA) spectral radiance from the Greenland ice sheet surface than was predicted using apparent reflectance spectra from the nadir-viewing spectrometer. While more investigation is required to convert airborne VSWIR spectral radiance into atmospherically corrected airborne surface reflectance, it is expected that airborne science flight data products will contribute to spectroscopic determination of Greenland ice sheet surface optical properties to improve understanding of their potential influence on ICESat-2 measurements.

Christopher J. Crawford↗

Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery

A two-stage predictive method was developed for lossless compression of calibrated hyperspectral imagery. The first prediction stage uses a conventional linear predictor intended to exploit spatial and/or spectral dependencies in the data. The compressor tabulates counts of the past values of the difference between this initial prediction and the actual sample value. To form the ultimate predicted value, in the second stage, these counts are combined with an adaptively updated weight function intended to capture information about data regularities introduced by the calibration process. Finally, prediction residuals are losslessly encoded using adaptive arithmetic coding. Algorithms of this type are commonly tested on a readily available collection of images from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral imager. On the standard calibrated AVIRIS hyperspectral images that are most widely used for compression benchmarking, the new compressor provides more than 0.5 bits/sample improvement over the previous best compression results. The algorithm has been implemented in Mathematica. The compression algorithm was demonstrated as beneficial on 12-bit calibrated AVIRIS images.

Kiely, Aaron B.↗

The cosmic microwave background radiation

Because angular anisotropies and spectral distortions of the cosmic microwave background radiation are judged to be inevitable at some level, in a realistic cosmological model, the evidence for spectral distortions and its theoretical implications are described. The evidence for anisotropy is then discussed, and theoretical predictions of radiation anisotropy are summarized and compared with the data available. It is found that spectral distortions at the 3-sigma level near the peak of the blackbody spectrum, although inconsistent with the predicted distortions due to Compton scattering in the early universe, are elegantly interpreted in terms of radiation from an early, pregalactic generation of massive stars which had been thermalized by a modest amount of dust at high redshift. The quadrupole anisotropy at the 4-sigma level is most simply interpreted in terms of the large-scale structure of the universe.

Silk, J.↗

Remote Sensing of smoke and its Direct Radiative Forcing in South America

Smoke aerosol, organic and black carbon particles suspended in the air, can absorb and reflect solar radiation to space, i.e., direct radiative forcing. Depending on the ratio of scattering to absorption, and the surface spectral properties, the net smoke effect can be warming or cooling of the climate system. Data from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) flown on the ER-2 at altitude of 20km, and of the AERONET ground based sun/sky radiometers are used to assess the smoke aerosol optical thickness over the land and the direct radiative forcing at the top of the atmosphere and at ground level, respectively. The data are collected during the Smoke, Clouds, and Radiation - Brazil (SCAR-B) experiment. In contrast to model results of the smoke effect, we show using the AVIRIS data, that even though the surface albedo is high (0.17 - average on the solar spectrum) and the smoke single scattering albedo is low (0.88), smoke does increase the instantaneous reflectance of sunlight to space by 30-40 W/m2 for an increase in the smoke optical thickness of 0.5. The AERONET data are used to derive, simultaneously, the effect of smoke on the downward radiation. Models using spectrally averaged smoke optical properties and averaged surface reflectance, predicted very small smoke forcing. The reason is that smoke is mainly opaque in short wavelengths (e.g.<0.7 micron) while the surface is mainly bright in longer wavelengths (>0.7 micron). Modeling the effect of smoke on climate forcing cannot be done using the spectrally average properties. It requires the knowledge of the smoke and surface spectral properties.

Kaufman, Yoram J.↗

Remote Sensing of Smoke and its Direct Radiative Forcing in South-America

Smoke aerosol, organic and black carbon particles suspended in the air, are capable to absorb and reflect solar radiation to space - direct radiative forcing. Depending on the ratio of scattering to absorption, and on the surface spectral properties, the net smoke effect can be warming or cooling of the climate system. Data from the AVIRIS spectrometer flown on the ER-2 at altitude of 20 km, and of the AERONET ground based sun/sky radiometers are used to assess the smoke aerosol optical thickness over the land and the direct radiative forcing at the top of the atmosphere and at ground level, respectively. The data are collected during the SCAR-B experiment in Brazil. In contrast to model results of the smoke effect, we show using the AVIRIS data, that even though the surface albedo is high (0.17 - average on the solar spectrum) and the smoke single scattering albedo is low (0.88), smoke does increase the instantaneous reflectance of sunlight to space by 30-40 W/m(exp 2) for an increase in the smoke optical thickness of 0.5. The AERONET data are used to derive, simultaneously, the effect of smoke on the downward radiation. Models using spectrally averaged smoke optical properties and averaged surface reflectance, predicted very small smoke forcing. The reason is that smoke is mainly opaque in short wavelengths (e.g.< 0.7 micron) while the surface is mainly bright in longer wavelengths (> 0.7 micron). Modeling the effect of smoke on climate forcing cannot be done using the spectrally average properties. It requires the knowledge of the smoke and surface spectral properties.

Kaufman, Yoram↗

PROSPECT: A Precision Reactor Oscillation and Spectrum Experiment

Nuclear reactors are a source of copious amounts of electron antineutrinos. They are emitted in the beta decays of the fission products and their energies depend on the isotopic composition of the reactor. In recent years a number of reactor antineutrino experiments including Daya Bay, Double Chooz, and RENO reported a deficit in the measured flux of antineutrinos from reactors compared to expectation and a spectral deviation in the measured energy spectra compared to model predictions. These observations led to the hypothesis of sterile neutrino oscillation as an explanation of the flux deficit. New physics or incomplete nuclear models may explain the origin of the spectral deviation. PROSPECT, the Precision Reactor Oscillation and Spectrum Experiment, is a novel neutrino experiment at the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL) designed to address two major scientific objectives: 1. Perform a search for eV-scale sterile neutrinos independent of reactor neutrino models by searching for the oscillation signature of massive, sterile neutrino states beyond the 3 known active neutrino species. The discovery of sterile neutrinos would indicate a new form of matter and require physics beyond the Standard Model. 2. Perform the first modern precision measurement of the antineutrino spectrum from a Highly Enriched Uranium (HEU) 235 U reactor to benchmark our understanding of the neutrino emission from nuclear reactors and to understand the isotopic origin of spectral deviations observed in previous reactor neutrino experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A linear shock cell model for non-circular jets using conformal mapping with a pseudo-spectral hybrid scheme

The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.

Bhat, Thonse R. S.↗

On the Origin and Evolution of Stellar Chromospheres, Coronae and Winds

The final report discusses work completed on proposals to construct state-of-the-art, theoretical, two-component, chromospheric models for single stars of different spectral types and different evolutionary status. We suggested to use these models to predict the level of the "basal flux", the observed range of variation of chromospheric activity for a given spectral type, and the decrease of this activity with stellar age. In addition, for red giants and supergiants, we also proposed to construct self-consistent, purely theoretical, chromosphere-wind models, and investigate the origin of "dividing lines" in the H-R diagram. In the report, we list the following six specific goals for the first and second year of the proposed research and then describe the completed work: (1) To calculate the acoustic and magnetic wave energy fluxes for stars located in different regions of the H-R diagram; (2) To investigate the transfer of this non-radiative energy through stellar photospheres and to estimate the amount of energy that reaches the chromosphere; (3) To identify major sources of radiative losses in stellar chromospheres and calculate the amount of emitted energy; (4) To use (1) through (3) to construct purely theoretical, two-component, chromospheric models based on the local energy balance. The models will be constructed for stars of different spectral types and different evolutionary status; (5) To explain theoretically the "basal flux", the location of stellar temperature minima and the observed range of chromospheric activity for stars of the same spectral type; and (6) To construct self-consistent, time-dependent stellar wind models based on the momentum deposition by finite amplitude Alfven waves.

Musielak, Z. E.↗

Observation and Modeling of the Solar Transition Region: A Quasi-Static Loops Model with Implications for Heating the Lower Transition Region - 1

We report on observations of the solar atmosphere in several extreme ultraviolet and far-ultraviolet bandpasses obtained by the Multi-Spectral Solar Telescope Array, a rocket borne spectroheliograph, on flights in 1987, 1991, and 1994, spanning the last solar maximum. Quiet sun emission observed in the 171 A - 175 A bandpass, which includes lines of 0Ov, O vi, Fe ix, and Fe x, has been analyzed to test models of the temperatures and geometries of the structures responsible for this emission. Analyses of intensity variations above the solar limb reveal scale heights consistent with a quiet sun plasma temperature of 500 000 K less than or equal to T(sub e) less than or equal to 800 000 K. Intensity modulations in the quiet sun are observed to occur on a scale comparable to the supergranular scale. The structures responsible for the quiet sun EUV emission are modeled as small quasi-static loops. We find that the emission predicted by loop models with maximum temperatures between 700 000 K and 900 000 K are consistent with our observations. We also present a preliminary comparison of the predictions of our models with observations of diagnostic spectral line ratios obtained from previous observers. We discuss the implications a distribution of loops of the type we model here would have for heating the lower transition region. Finally, in fight of the models we calculate here, we briefly review the current state of knowledge concerning the contributions thermal conduction from coronal (T(sub e) greater than or equal to 10(exp 6) K) and upper transition region (10(exp 5) K less than T(sub e) less than 10(esp 6) K) structures make to lower transition region emission. We argue that the evidence which has lead many authors to conclude that the interface of hotter and cooler plasmas makes a negligible contribution to lower transition region emission is much less compelling in light of recent observations and analyses. We further argue that it is the interface of chromospheric material with structures such as loops that have sub-coronal peak temperatures (i.e. less than 900 000 K) that makes the dominant contribution to lower transition region emission in the quiet sun.

Oluseyi, Hakeem M.↗

Advanced Graphite Creep Uncertainty Analysis

Radiation damage estimation is an important component of the post irradiation analysis of the Advanced Graphite Creep (AGC) experiment. It depends primarily on the fast fluence, which is determined using well established methods of spectral adjustment. These are based on best estimates from models such as Monte Carlo N-Particle (MCNP), input cross-sections, and measured activities from flux wires in the experiment. Each of these parameters can propagate uncertainties which will affect the uncertainty in the calculated dose levels for AGC, or any experiment irradiated within a reactor. While the methods of propagating uncertainty are well-established, the final uncertainty estimates they provide are only as good as the estimates of uncertainty in the inputs on which they are based. The purpose of this work is to outline some deficiencies in the ways these input uncertainties are presently estimated, and to outline a methodology by which they can be improved. The fast fluence and radiation damage received by graphite specimens irradiated in the Advanced Graphite Creep (AGC) experiments is presently estimated using spectral adjustment methods that are based on both flux wire activity measurements, and MCNP model predictions. This work describes an ongoing effort to quantify and propagate uncertainties in inputs to the spectral adjustment process, and thereby quantify the resultant error in radiation damage (dpa) estimates. The effort is multi-faceted, and we consider the impacts of both the set of flux wires selected, and the counting process. An expanded set of flux wires is identified that provides a more comprehensive data set on the fast spectrum. To address the counting process itself, a series of round-robin measurements in several reactor metrology laboratories across the Department of Energy (DOE) complex and nuclear industry are being undertaken to refine the American Society for Testing and Materials (ASTM) standards for flux wire measurements. To address the contribution of uncertainty in the MCNP model predictions, an uncertainty quantification (UQ) tool has been developed that statistically samples the model input parameters, runs a series of cases, and assimilates the results to provide an overall uncertainty. The impact of the MCNP UQ tool results is demonstrated by re-analyzing previous AGC flux wire and irradiation data. While the expanded flux wire set obviously cannot be added to these experiments retroactively, plans for future graphite irradiations are outlined.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Practical Guide to Chemometric Analysis of Optical Spectroscopic Data

The methodology and mathematical treatment of several classic multivariate methods for the analysis of spectroscopic data is demonstrated in a straightforward way that can be used as a basis for teaching an undergraduate introductory course on chemometric analysis. The multivariate techniques of classical least squares (CLS), principal component regression (PCR), and partial least squares (PLS), as well as the univariate Beer’s law method have been described and compared, building students’ understanding by starting with the univariate method and progressing step by step into the multivariate methods. Equations for the production of regression vectors from training set spectral data is described and their use demonstrated for the prediction of constituent concentrations on a separate validation set of spectra. Extreme care is taken to ensure consistency in variable formatting of data matrices. This provides a key foundation to understanding how spectral data are manipulated using these different mathematical approaches for building quantitative regression models. Each method is applied to a real-world data set, and the results are discussed to show students the types of information that can be gleaned from each method. A training set comprised of 20 infrared absorbance spectra containing 3 constituents (benzene, polystyrene, and gasoline) of known composition are used to demonstrate the matrix operations for each regression method. A separate set of 12 real-world napalm samples (containing benzene, polystyrene and gasoline) are used as a validation set to demonstrate the ability to utilize the regression models on an unknown dataset. A toolbox (PNNL Chemometric Toolbox) written in MATLAB language is supplied in the Supplemental Information file and can be used as a companion for understanding the development and deployment of the chemometric algorithms described in this paper. The datasets of the infrared spectra are also supplied, allowing users to build and inspect the chemometric models on their own. Finally, the Toolbox includes scripts to assist users in loading their own datasets into MATLAB and performing CLS, PCR, and PLS on their data.

Upper-Division Undergraduate, Analytical Chemistry↗

Experiments and Analyses of Distributed Exhaust Nozzles

Experimental and analytical aeroacoustic properties of several distributed exhaust nozzle (DEN) designs are presented. Significant differences between the designs are observed and correlated back to Computational Fluid Dynamics (CFD) flowfield predictions. Up to 20 dB of noise reduction on a spectral basis and 10 dB on an overall sound pressure level basis are demonstrated from the DEN designs compared to a round reference nozzle. The most successful DEN designs acoustically show a predicted thrust loss of approximately 10% compared to the reference nozzle. Characteristics of the individual mini-jet nozzles that comprise the DEN such as jet-jet shielding and coalescence are shown to play a major role in the noise signature.

Kinzie, Kevin W.↗

Impact of intermolecular interactions on the spectroscopic signals, energetics, and redox behavior of high valent 237 Np (Final Report)

Our studies have led to definitive spectral assignments for neptunyl-neptunyl interactions in aqueous solutions that will be valuable for predicting Np(V) speciation in solution. We have definitively demonstrated how actinyl-hydrogen and actinyl-cation interactions can influence spectral features for uranyl and neptunyl system. In addition, we have developed DFT methodologies to predict enthalpies of formation for uranyl and neptunyl systems and linked stability to chemical descriptors (hydrogen interaction energies or the electrostatic attraction energies). The counterion influenced the rate of Np(V) oxidation to Np(VI) neptunates and [Np(VII)O 4 OH] 3- complexes. Oxidation to Np(VII) during ozonolysis takes place through the presence of hydroxyl radicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Empirical Cumulus Parameterization Scheme for a Global Spectral Model

Realistic vertical heating and drying profiles in a cumulus scheme is important for obtaining accurate weather forecasts. A new empirical cumulus parameterization scheme based on a procedure to improve the vertical distribution of heating and moistening over the tropics is developed. The empirical cumulus parameterization scheme (ECPS) utilizes profiles of Tropical Rainfall Measuring Mission (TRMM) based heating and moistening derived from the European Centre for Medium- Range Weather Forecasts (ECMWF) analysis. A dimension reduction technique through rotated principal component analysis (RPCA) is performed on the vertical profiles of heating (Q1) and drying (Q2) over the convective regions of the tropics, to obtain the dominant modes of variability. Analysis suggests that most of the variance associated with the observed profiles can be explained by retaining the first three modes. The ECPS then applies a statistical approach in which Q1 and Q2 are expressed as a linear combination of the first three dominant principal components which distinctly explain variance in the troposphere as a function of the prevalent large-scale dynamics. The principal component (PC) score which quantifies the contribution of each PC to the corresponding loading profile is estimated through a multiple screening regression method which yields the PC score as a function of the large-scale variables. The profiles of Q1 and Q2 thus obtained are found to match well with the observed profiles. The impact of the ECPS is investigated in a series of short range (1-3 day) prediction experiments using the Florida State University global spectral model (FSUGSM, T126L14). Comparisons between short range ECPS forecasts and those with the modified Kuo scheme show a very marked improvement in the skill in ECPS forecasts. This improvement in the forecast skill with ECPS emphasizes the importance of incorporating realistic vertical distributions of heating and drying in the model cumulus scheme. This also suggests that in the absence of explicit models for convection, the proposed statistical scheme improves the modeling of the vertical distribution of heating and moistening in areas of deep convection.

Rajendran, K.↗

Multiscale turbulence effects in underexpanded supersonic jets

A modified version of the multiscale turbulence model of Hanjalic has been applied to the problem of underexpanded supersonic jets. In particular, the shock-cell decay resulting from shock-mixing layer interactions has been studied for both mildly interacting and strongly resonant jet conditions. A version of the Hanjalic model which accounts for nonequilibrium energy transfer between two spectral scales of turbulence was incorporated into an existing shock-capturing, parabolized Navier-Stokes computational model in order to perform numerical experiments. Results are presented for nominal initial jet Mach numbers of 2.0, 1.4, and 1.0 and are compared to experiments and to predictions made using single-scale models. The results show significant effects of multi-spectral turbulent energy transfer on the predicted shock-cell decay particularly for the lower jet Mach numbers.

Abdol-Hamid, Khaled S.↗