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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Modeling of small tungsten dust grains in EAST tokamak with NDS-BOUT ++

In order to investigate the transport of small dusts as well as their evolution property along their trajectories, the NDS module is developed under the BOUT++ framework, a highly desirable C++ code package to perform parallel plasma fluid simulations with an arbitrary number of equations in three-dimensional curvilinear coordinates. Due to the severe dust ablation in fusion plasmas, the dust size would decrease from micrometer to nanometer, resulting in impurities. Small dusts in the simulations here are specified as tungsten spheres with the radii on or below the order of submicrometer. The Rayleigh limit is included in the charging process when the dust is ablated to the droplet phase. The simulation results from the NDS module show that a 200 nm radius spherical tungsten dust originated from upper divertor region of EAST Tokamak is ablated completely due to the intense heating from the incoming plasma inside the core region, well consistent with the CCD footage of EAST shot # 81459. Furthermore it is found that the magnetic field dominates the dust transport when the dust radius is below 100 nm during the ablation along the trajectory. Our simulations predict that a 10 nm radius spherical tungsten dust injected from the inner midplane is well constrained by the magnetic field, and it reaches the inner divertor target with a velocity on the order of km/s.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Microwave-assisted catalytic gasification of mixed plastics and corn stover for low tar, hydrogen-rich syngas production

The challenge for efficient management of post-consumer plastic and biomass waste has grown over the past few decades due to their dramatic increases. In comparison to conventional gasification, microwave-assisted co-gasification of plastics and corn stover offers many benefits, including increased H 2 yield and gas components compared to unfavorable char/tar. Nonetheless, for future commercialization of the process and ease of product separation, further reduction of the undesirable tar is necessary, which can be achieved over the catalytic route. Here, in this work, we studied the catalytic effect of magnetite for microwave-assisted co-gasification of corn stover and plastic to make syngas with higher H 2 and lower tar selectivity over non-catalytic conditions. A 1:1:1 ratio of plastic-corn stover-magnetite was used to evaluate the reaction parameters such as temperature, space velocity, heating media, and catalytic cycles under gasification conditions. In comparison with the microwave non-catalytic route, a 100% increase in the total H 2 yield with 76% higher H 2 production efficiency (mmol/kWh) was achieved in the presence of the magnetite catalyst, while reducing the overall tar formation from 9% to 2%. When magnetite was reduced in situ during the reaction, it coupled with microwave and delivered oxygen radicals that cracked down plastic and corn stover intermediates generated from the synergistic effect under microwave heating. Soon after the oxygen transfer process initiated, magnetite reached its final oxidation state consisting of microwave-active Fe and Fe 3 C phases that continued coupling with microwaves along with the generated graphitic carbon to maintain the heat necessary to further reduce the generated tar and make additional gaseous products, as confirmed by XRD, Raman, and TGA analyses.

08 HYDROGEN↗
DOE OSTI2022

Elucidating the challenges in extracting ultra-slow flame speeds in a closed vessel - A CH 2 F 2 microgravity case study using optical and pressure-rise data

Refrigerants with a low global warming potential (GWP) possess mild flammability. Hence, a fundamental understanding of their combustion characteristics is required to assess their fire-hazardous potential. The laminar burning velocity is one fundamental property to describe these under safety evaluation aspects. However, measuring laminar burning velocities for slow-burning components, such as low-GWP alternatives, is challenging. This is due to influencing effects such as buoyant flame deformation, stretch, radiation, and confinement, especially at the flammability limits. Here, in the present study, we investigated near-limit flames of the representative refrigerant difluoromethane (CH 2 F 2 ) with nitrogen-enriched oxidizer mixtures to elucidate the potentials and limitations at ultra-slow flame speeds of two widely used flame speed measurement methods in the closed vessel configuration: the optical flame speed measurement in the early quasi-isobaric regime and the flame speed determination from the pressure-rise during the later phase of the isochoric combustion process. Experiments were performed under terrestrial- and microgravity, conducted in a specially designed setup suitable for drop tower applications, using both methods in parallel. Recommendations for the extraction of flame speed data are derived from the non-buoyant reference investigations under microgravity and transferred to ultra-slow flames at terrestrial gravity. Near-limit flames under microgravity were found to be significantly affected by stretch effects for the optical method so that flame speed extrapolations to unstretched conditions are prone to errors. Stretch also affects the pressure method’s lower evaluation limit, and errors can be estimated by combining flame speed data from the pressure method and Markstein lengths from optical experiments.

42 ENGINEERING↗
DOE OSTI2022

High Resolution Photoelectron Spectroscopy of the Acetyl Anion

High-resolution photoelectron spectra of cryogenically cooled acetyl anions (CH 3 CO - ) obtained using slow photoelectron velocity-map imaging are reported. The high resolution of the photoelectron spectrum yields a refined electron affinity of 0.4352 ± 0.0012 eV for the acetyl radical as well as the observation of a new vibronic structure that is assigned based on ab initio calculations. Three vibrational frequencies of the neutral radical are measured to be 1047 ± 3 cm -1 (ν 6 ), 834 ± 2 cm -1 (ν 7 ), and 471 ± 1 cm -1 (ν 8 ). Here this work represents the first experimental measurement of the ν 6 frequency of the neutral. The measured electron affinity is used to calculate a refined value of 1641.35 ± 0.42 kJ mol -1 for the gas-phase acidity of acetaldehyde. Analysis of the photoelectron angular distributions provides insight into the character of the highest occupied molecular orbital of the anion, revealing a molecular orbital with strong d-character. Additionally, details of a new centroiding algorithm based on finite differences, which has the potential to decrease data acquisition times by an order of magnitude at no cost to accuracy, are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Properties of a fading AGN from SDSS-IV MaNGA

ABSTRACT We identify a fading AGN SDSS J220141.64+115124.3 from the internal Product Launch-11 (MPL-11) in Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. The central region with a projected radius of $\sim$2.4 kpc is characterized as LINER-like line ratios while the outskirts extended to $\sim$15 kpc show Seyfert-like line ratios. The ${\rm{[O {\small III}]}}$$\lambda$5007 luminosity of the Seyfert regions is a factor of 37 (2) higher than the LINER regions without (with) dust attenuation correction, suggesting that the AGN activity decreases at least $\sim$8 $\times$ 10$^3$ yr ($\sim$2.4 kpc/light-speed) ago. We model the emission line spectra in the central region with double Gaussian components (a narrow core and a broad wing) and analyse the properties of each component. The narrow core component mostly co-rotates with the stellar disc, whereas the broad wing component with a median of the velocity dispersion $\sim$300 km s$^{-1}$ is related to a wind outflow. The kinematic position angle (PA) of the ionized gas shows an $\sim 20^{\circ }$ twist from the galaxy centre to 1.5 effective radius. The median of the PA difference between the gas and stellar components is as large as $\sim 50^{\circ }$ within 0.4 effective radius. The tidal feature in DESI image and star–gas misalignment suggest this galaxy is a merger remnant. Combining all these observational results as well as public available X-ray and MIR luminosities, we confirm this is a fading AGN, the merger process kick-started the central engine to quasar phase which ionized gas composed of tidal debris, and now the activity of the central black hole decreases. The discontinuity in ${\rm{[O {\small III}]}}$$\lambda$5007 flux and EQW maps is due to multiple AGN outbursts triggered by merger remnant gas inflows.

Mo, Hao (ORCID:0000000234430768)↗
DOE OSTI2023

Unsupervised Learning Based Interaction Force Model for Nonspherical Particles in Incompressible Flows

This project provides a neural network-based interaction force model for gas-solid flows from low to intermediate Reynolds numbers and concentration, which can be linked to MFiX-DEM. We have constructed a database of the interaction force between the irregular-shaped particles using a spherical harmonic method and the fluid phase based on the particle-resolved direct numerical simulation (PR-DNS) with immersed boundary-based gas kinetic scheme. Unsupervised learning method, i.e., variational auto-encoder (VAE) has been applied to extract the primitive shape factors determining the drag force, lifting forces, and torque. The interaction force model has been trained and validated with a simple but effective multi-layer feed-forward neural network: multi-layer perceptron (MLP), which will be concatenated after the encoder of the previously trained VAE for geometry feature extraction for single, irregular particles. We have trained transpose convolutional neural networks with the PR-DNS data to predict the velocity and pressure gradient of the single particle systems and utilized them to calculate drag force of multi-particle systems. This model can provide high computational efficiency because it does not require collecting multiparticle system data from PR-DNS.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

The Onset of Nucleate Boiling Prediction in a Mini Channel with the Eulerian Multiphase Flow

The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Damage initiation and evolution in Al-Si layered microstructures under shock loading conditions at atomic scales

Designing materials with microstructural features like multiphase interfaces have shown significant promise for usage in the next generation defense and nuclear applications. The dynamic response of these interfaces in extreme environments is observed to vary with the deformability of individual phases, which could subsequently alter the favored damage nucleation sites related to spall failure. Here, we investigate the role of spacing of interfaces in a nanocrystalline layered Aluminum-Silicon system on the shock wave propagation behavior, and microstructural and defect evolution using classical molecular dynamics simulations. The simulations are carried out with different hypothetical Al/Si microstructures including variations in the distribution of Si grains as layers in a nanocrystalline Al matrix. The molecular dynamics simulations suggest that spall failure is preferentially initiated at Al/Si interfaces. In addition, for the same system volume and same concentration of Si, a higher number of layers is marked by an increase in shock wave velocity and reduced resistance to spall failure.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Counter-propagating toroidal Alfvén eigenmodes in tokamaks

Mechanisms of destabilization of toroidal Alfvén eigenmodes (TAEs) in tokamaks are analyzed with the aim to reveal those leading to modes propagating in the direction opposite to plasma current, i.e. counter-propagating modes (ctr-TAE). Plasmas with fast-ions sources [such as neutral beam injection (NBI), ion cyclotron resonance heating, fusion reactions] and without them (Ohmic discharges) are considered. A particular NSTX-U experiment with NBI, where co- and counter-propagating TAEs were observed simultaneously (Podestà et al 2018 Nucl. Fusion 58 082023), is considered. It is concluded that both types of TAEs occurred because their destabilization was caused by the velocity anisotropy of beam ions, which overrode effects of spatial inhomogeneity of these ions.

Alfvénic instabilities↗
DOE OSTI2023

Colliding localized, lumpy holographic shocks with a granular nuclear structure

We apply a recent and simple technique which speeds up the calculation of localized collisions in holography to study more realistic models of the pre-hydrodynamic phase of heavy ion collisions using gauge/gravity duality. Our initial data reflects the lumpy nuclear structure of real heavy ions and our projectiles’ aspect ratio mimics the Lorentz contraction of nuclei during RHIC collisions. At the hydrodynamization time of the central region of the quark gluon plasma developed during the collision, we find that most of the system’s vorticity is located well outside the hydrodynamized part of the plasma. Only the relativistic corrections to the thermal vorticity within the hydrodynamized region are non-negligible. We compare the transverse flow shortly after the collision with previous results which did not use granular initial conditions and determine the proper energy density and fluid velocity in the hydrodynamized subregion of the plasma.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Weak-Bonding Elements Lead to High Thermoelectric Performance in BaSnS 3 and SrSnS 3 : A First-Principles Study

SnS2, an earth-abundant and ecofriendly material, is limited as a thermoelectric material because of the high lattice thermal conductivity κ L and low carrier mobility μ. By introducing weak-bonding elements Ba or Sr into the SnS 2 framework, we discovered two SnS 2 -based materials BaSnS3 and SrSnS3 with the calculated low κL values of 0.15 and 0.17 W m -1 K -1 , respectively, along the a-axis. The low group velocity and high lattice anharmonicity originating from the weakened and distorted Sn–S bonding network are found in both systems. Moreover, the vibrations of Ba and Sr induce low-lying optical phonons, which strongly couple with the acoustic phonons and strengthen the phonon scattering rates. Compared to SnS 2 , both compounds present lower single-band effective masses, smaller deformation potential constants, and better band convergence, which enhance μ with an insignificantly reduced effective mass. By solving the linearized Boltzmann transport equation with a nonempirical carrier lifetime, we predict excellent ZT values of 2.89 and 2.77 along the a-axis at 900 K in BaSnS 3 and SrSnS 3 , respectively. Further phase diagram calculations of Ba 1–x Sr x SnS 3 solid solutions propose a new compound, Ba 0.5 Sr 0.5 SnS 3 , with an even higher ZT of 3.0. Our work analyzes explicitly how weak-bonding elements enhance μ and suppress κL simultaneously in SnS 2 -analogous systems with a series of compounds nominated as potential high-performance thermoelectric materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

In-Situ Blade Strain Measurements of a Crossflow Turbine Operating in a Tidal Flow

This data was collected between October 25 and December 12 of 2022 at the University of New Hampshire (UNH) and Atlantic Marine Energy Center (AMEC) turbine deployment platform (TDP). The goal was to collect blade strain data from a crossflow turbine operating in a tidal flow. A table in ('Deployment Schedule.PNG') outlines the various dates when each instrument was operational, and more details can be found via literature listed in 'Related Publications'.txt. This dataset includes zipped folders for each instrument containing data in .csv files for the relevant duration specific to each instrument, along with separate README file for each measurement. Some instrument files are quite large and can pose a challenge for a visual spreadsheet editor to open. A processing software like MATLAB or Python is recommended. All data contained in this submission is unfiltered/unprocessed data unless otherwise noted in the README file. Blade strain was measured using 8 foil-based strain gauges along the span of a single turbine blade. Water currents were measured using Acoustic Doppler Current Profilers (ADCP's) and Acoustic Doppler Velocimeters (ADV's) both upstream and downstream of the turbine for inflow, wake and turbulence measurements. Electrical power output was measured using the Voltsys rectifier. Shaft speed was calculated based on the Voltsys measurements of the permanent magnet three phase generator AC generation frequency, coupled directly to the cross flow turbine under test (i.e., no gear box). Platform motions were captured using a Yost IMU (inertial measurement unit). Turbine thrust loading was measured using a reaction arm about the turbine deployment platform spanning beam, where two bi-directional load cells were connected to the system via a pinned connection. The TDP is a floating structure moored on the Portsmouth facing side of Memorial Bridge pier #2, which spans the Piscataqua River between Portsmouth, NH and Kittery, ME. The Piscataqua River connects the Great Bay Estuary to the Gulf of Maine and the river currents are dominated by tidal flow with water velocities exceeding 2.5 m/s during spring ebb tides at this site which were previously characterized by Chancey 2019. The turbine under test was a modified New Energy Corporation (Calgary, CA) model EVG-025 4-blade H-Darrius type vertical axis cross flow turbine that rotates in the clockwise direction with a rotor diameter of 3.2m and blade length of 1.7m. The hydro-foil profile was a NACA 0021 with a 10 inch chord length and a blade preset pitch angle of +4deg with a positive angle corresponding with the toe in direction. The standard EVG-025 has a rotor diameter of 3.4m and its rated power output is 25kW at 3 m/s. The rotor diameter was reduced to accommodate the size of the existing TDP moon-pool. A single blade of this turbine was further modified to accommodate 8 full-bridge strain gauges (Bharath et al 2023, Bichanich et al 2024). For power performance and other relevant details on the turbine and its characteristics, see O'Byrne 2022.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Transport Properties of Magnetized High-Energy Density Plasma (Final Project Report)

This report summarizes results of project DE-SC0016159 "Transport Properties of Magnetized High-Energy-Density Plasma,'' which ran from 7/15/2016 - 7/14/2021. The primary objectives of the work, as stated in the original proposal, were to develop a theory that describes transport coefficients in magnetized high energy density plasmas and to test the theory with molecular dynamics (MD) simulations. The science challenge is that strong ion coupling, strong magnetization of electrons, and partial degeneracy of electrons, cause the system to be in a regime that is not well described by current theory. The particular processes that were to be investigated include: ion stopping power, diffusion, electron-ion temperature relaxation, thermal conduction and viscosity. All of the primary research objectives were accomplished during the course of this work. In addition, some unexpected results were discovered along the way that led to new and productive research directions. This work resulted in 17 publications in well-respected peer-reviewed journals (primarily Physics of Plasmas and Physical Review E), and 2 more are being prepared for publication. A few of these were selected as Editor's Picks and one was published as a Rapid Communication. Highlights of the research results include: Transport phase space: The first identification of the parameter space that defines fundamental transport regimes in terms of the Coulomb coupling and magnetization parameters. Mean force kinetic theory: Systematic derivation of a kinetic theory for strongly coupled plasmas based on a new expansion parameter of the BBGKY hierarchy. This provided the derivation of a theory that we had previously posed phenomenologically, and also revealed a new term that captures the equation of state properties at all coupling strengths. Transverse friction force: Discovery that the friction force on a test charge in a strongly magnetized plasma includes a component that is perpendicular to the motion of the test charge in the plane defined by the velocity and magnetic field vectors. Gyrofriction force: Discovery that the friction force on a test charge in a plasma that is both strongly magnetized and strongly coupled includes a component of the force in the direction of the Lorentz force. Kinetic theory for warm dense matter: Extension of the mean force kinetic theory to include partial electron degeneracy, so that it applies to warm dense matter.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Phase-space sensitivity (weight functions) of 3 MeV proton diagnostics

Abstract The weight function W ( X ) is a diagnostic sensitivity to phase-space variables X that relates the measured signal C to the distribution function F ( X ) through the equation C = ∫ W ( X ) F ( X ) d X . In the present work, an algorithm to calculate W for a diagnostic that measures 3 MeV protons produced in d(d,p)t fusion reactions between a fast ion and a thermal deuteron is developed. The emitted protons escape the tokamak on curved orbits and are detected. These curved orbits constitute effective diagnostic ‘sightlines’. The presented algorithm accounts for the complications associated with these curved sightlines. An initial calculation of time-reversed proton orbits computes effective solid angles and sightlines for the relevant range of incident proton velocity vectors. These precomputed orbits are then used within the framework of FIDASIM (2020 Plasma Phys. Cont. Fusion 62 105008) to calculate the reactivity averaged over the thermal distribution of the ‘target’ deuterons and the probability that a fast ion of specified energy and pitch has a gyroangle that is consistent with the kinematic equations along each of the sightlines. Comparisons with analytic formulas and with independent calculations for the Mega Amp Spherical Tokamak 3 MeV proton diagnostic verify the algorithm.

Physics↗
DOE OSTI2020

Collaborative investigation of the internal flow and near-nozzle flow of an eight-hole gasoline injector (Engine Combustion Network Spray G)

The internal details of fuel injectors have a profound impact on the emissions from gasoline direct injection engines. However, the impact of injector design features is not currently understood, due to the difficulty in observing and modeling internal injector flows. Gasoline direct injection flows involve moving geometry, flash boiling, and high levels of turbulent two-phase mixing. In order to better simulate these injectors, five different modeling approaches have been employed to study the engine combustion network Spray G injector. Here these simulation results have been compared to experimental measurements obtained, among other techniques, with X-ray diagnostics, allowing the predictions to be evaluated and critiqued. The ability of the models to predict mass flow rate through the injector is confirmed, but other features of the predictions vary in their accuracy. The prediction of plume width and fuel mass distribution varies widely, with volume-of-fluid tending to overly concentrate the fuel. All the simulations, however, seem to struggle with predicting fuel dispersion and by inference, jet velocity. This shortcoming of the predictions suggests a need to improve Eulerian modeling of dense fuel jets.

ECN↗
DOE OSTI2025

Catalytic water splitting kinetics and optimization

This project was motivated primarily by the opportunity of turning photocatalysis into a cost efficient hydrogen generation method for domestic energy and chemical production, and by the need to provide detailed mechanisms of photocatalytic reactions of broad scientific and technological interest. Specifically, we focused on the development of a new technique for analysis of (photo)catalytic reaction mechanisms to guide photocatalyst design. Our approach was based on applying velocity map imaging (VMI) to surface catalyzed reactions in order to identify photocatalytic reaction products, intermediates, and relate these to photocatalyst composition, dimensions, size and other characteristics. By coupling VMI with other spectroscopic and microstructural characterization, we aimed to reveal the features that limit performance of photocatalysis. As a first step to achieve this goal, we constructed a custom VMI microscope specifically designed for investigation of surface photocatalytic reactions and validated it’s design using a photodissociatinon of MnBr(CO) 5 adsorbed on a metallic surface. Using both 230 nm and 266 nm pulsed laser excitations, we observed that there are likely three main pathways for photodissociation of Mn(CO)5Br: from the gas phase, the surface, and ejected Mn complex from the surface increasing the gas phase concentration.

08 HYDROGEN↗
DOE OSTI2020

Multi-scale characterization and simulation of impact welding between immiscible Mg/steel alloys

Vaporizing foil actuator spot welding method is used in this paper to join magnesium alloy AZ31 and uncoated high-strength steel DP590, which are typically considered as un-weldable due to their high physical property disparities, low mutual solubility, and the lack of any intermetallic phases. Characterization results from scanning electron microscopy (SEM) and high-resolution transmission electron microscopy (HRTEM) of the weld interface indicate that the impact creates an Mg nanocrystalline interlayer with abundant Fe particles. The interlayer exhibits intact bonding with both DP590 and AZ31 substrates. To investigate the fundamental bond formation mechanisms at the interface, a finite element (FE)-based process simulation is first performed to calculate the local temperature and deformation at the interface under the given macroscopic experimental condition. Finally, taking the FE results at the interface as inputs, molecular dynamics (MD) simulations are conducted to study the interlayer formation at the Mg/Fe interface during the impact and cooling. The results found a high velocity shearing-induced mechanical mixing mechanism that mixes Mg/Fe atoms at the interface and creates the interlayer, leading to the metallurgical bond between Mg/steel alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability

In this work, a model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V 0 ∝ kh(k, 0) that eventually decays in time as 1/kV 0 t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude h rms (k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of kh rms for the initial spectrum is used to calculate a nonlinear factor F NL that reduces V 0 , as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝t θ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.

42 ENGINEERING↗