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DOE OSTI2020

Spall and subsequent recompaction of copper under shock loading

Research was undertaken to study spall and subsequent recompaction of oxygen-free high-thermal-conductivity copper using a single-stage large-bore light gas gun capable of planar impacts. Gun experiments were conducted that produced an initial spall in the target with a subsequent recompaction of the spall damage/layer by the use of layered impactors. Symmetric spall experiments at similar conditions were also conducted as a control to the recompaction experiments. Photonic Doppler velocimetry was used to obtain the velocity history of the target’s back surface; these velocity histories were analyzed, and the results were compared to numerical simulations. After recovery of selected samples, the microstructure was analyzed using optical imaging microscopy and electron backscatter diffraction. Recompaction waves were clearly observed in the time-resolved data obtained at the back surface of the targets. Two different series of experiments were performed to understand the effect of damage morphology on the stress required for spall recompaction. In the initial series, the peak pressure of the first shock was systematically increased to alter the amount of damage in the material. While in the second series, the peak pressure of the second shock was increased, keeping the magnitude of the first shock relatively constant to understand the effect of peak stress on the recompaction process. Findings clearly show that recompaction results in a perturbed band of the microstructure at the location of the expected spall plane in all cases except where the peak stress of the second shock is lower than the critical value.

, recompaction↗

DOE OSTI2021

Fuel convergence sensitivity in indirect drive implosions

In inertial confinement fusion experiments at the National Ignition Facility, a spherical shell of deuterium–tritium fuel is imploded in an attempt to reach the conditions needed for fusion, self-heating, and eventual ignition. Since theory and simulations indicate that ignition efficacy in 1D improves with increasing imploded fuel convergence ratio, it is useful to understand the sensitivity of the scale-invariant fuel convergence on all measurable or inferable 1D parameters. In this paper, we develop a simple isobaric and isentropic compression scaling model incorporating sensitivity to the in-flight adiabat inferred from shock strengths, to measured implosion velocity, and to known initial ablator and fuel aspect ratio and mass ratio. The model is first benchmarked to 1D implosion simulations spanning a variety of relevant implosion designs. We then use the model to compare compressibility trends across all existing indirect-drive layered implosion data from the facility spanning three ablators [CH, carbon (C), and Be], for which in-flight fuel adiabats varied from 1.6 to 5 by varying the number of drive shocks from 2 to 4, peak implosion velocities varied by 1.4×, capsule radii by 50%, and initial fuel aspect ratios by 1.4×. We find that the strength of the first shock is the dominant contributor setting the maximum fuel convergence. We also observe additional sensitivities to successive shock strengths and fuel aspect ratios that improve the agreement between the expected and measured compression for carbon and Be designs with adiabats above 3. A principal finding is that the adiabat 2.5 C-shell designs exhibit less convergence than CH-shell designs of similar inferred in-flight adiabat.

Landen, O. L. (ORCID:0000000214998217)↗

DOE OSTI2022

The Study on the Shock Wave Propagation Rule of a Gas Explosion in a Gas Compartment

Combined with the k-ε turbulence model of general application, a refined finite element model of a utility tunnel’s gas compartment filled with the methane/air mixture is developed. A series of analyses are made by using the powerful industry-leading computational fluid dynamics (CFD) software flame acceleration simulator (FLACS) to study the shock wave propagation rule in the gas compartment. The longitudinal and transversal distribution laws of the explosion shock wave are gained taking into consideration the spatial characteristics of the gas compartment. The influences of a few parameters, such as initial conditions and section size of the gas compartment, on the shock wave propagation rule are further discussed. The basic procedure for predicting the peak pressure of the blast wave is provided by considering the initial conditions and the gas compartment, and the corresponding injury effect of the explosion wave on the living beings is assessed. The investigation demonstrates that the peak pressure by the coupled effect between the initial conditions is significantly influenced, especially at the upper and lower gas explosion limits. The peak pressure increases gradually as the width or height increases, and both basically meet the linear relation. The proposed method can forecast the peak pressure of the explosion shock wave in the gas compartment accurately. According to the peak pressure longitudinal and transversal distributions of the blast wave, the peak pressure is far greater than the killing pressure threshold in the underground and closed space; consequently, it is not safe for the living beings in the gas compartment.

Lin, Shu-Chao↗

DOE OSTI2023

Electron Injection via Modified Diffusive Shock Acceleration in High-Mach-number Collisionless Shocks

The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Effects of sub‐mm cylindrical voids on detonation performance in PBX 9501

Abstract Internal features of varying scale and geometry are always present in explosives systems. Below a critical length, dependent on the explosive, these features can operate as a driving force for energy concentration and reaction, known as hotspots. At larger length scales, internal features result in jetting and detonation wave shaping, allowing for bulk work to be done by the explosive as is seen in shape charges. To date, a large volume of work has been performed to simulate hotspot ignition and large‐scale wave shaping. However, little experimental data exists on the effects of features in intermediate length scales, 0.1 to 1 millimeter. It has been observed in many tests that these small‐scale features can influence the high explosive (HE) performance and in some cases cause substantial damage to adjacent systems. This work provides quantitative data on the effects of machined voids moderately above more typical hotspot lengths, 0.3–0.8 mm in diameter, in PBX 9501 pressed to 1.785 g cm −3 ±2.5 mg cm −3 . Streak imaging was used to visualize void collapse, jet velocity, re‐initiation time, and wave shape evolution. Delay in detonation front propagation time was found to be linearly dependent on the void diameter and jet velocity was found to be independent within the tested range and resolution. Cut‐back experiments were used to investigate wave shape distortion and evolution downstream of the void, showing consistent growth and decay shapes across all void sizes. Simulations using CTH, a hydrocode by Sandia National Laboratory, were used to investigate void collapse showing agreement with the trends of experimental results but yielded inaccurate wave shape development delay values. Both simulation and experimental results identified several re‐initiation mechanisms with jetting and subsequent double shocking of localized HE being the dominant mechanisms for the void sizes that were studied.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Recent and planned hydrodynamic instability experiments on indirect-drive implosions on the National Ignition Facility

At National Ignition Facility (NIF), yield amplification due to alpha particle heating approached ~3 in the highest performing inertial confinement fusion (ICF) implosions, while yield amplification of ~15-30 is needed for ignition. Hydrodynamic instabilities are a major factor in degradation of implosions while understanding and mitigation of the instabilities are critical to achieving ignition. This article describes recent and planned hydrodynamic instability experiments with several focused platforms that have been developed to directly measure these instabilities in all phases of ICF implosions. Measurements of ripple-shock generation at OMEGA laser have indicated initial seeds for the instabilities in three ablators - plastic (CH), beryllium, and high-density carbon (HDC). Hydrodynamic Growth Radiography (HGR) platform was used to measure instability growth at the ablation front in the acceleration phase of implosions. This platform used pre-imposed 2-D perturbations for growth factor measurements at different perturbation wavelengths and was also used to measure growth of “native roughness” modulations, fill tubes, and capsule support membranes or “tents”. Also, in the acceleration phase several new experimental platforms have been or are being developed to measure instability growth at the ablator-ice interface. In the deceleration phase of implosions, “self-emission” and “self-backlighting” platforms were developed to measure perturbations near peak compression. This article reviews recent progress and results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

PETN Exploding Bridgewire (EBW) Detonators: A Review

Exploding bridgewire (EBW) detonators have been used in weapon systems since the 1940s but there is huge debate surrounding how energy is transferred throughout the EBW firing system and the mechanism by which the exploding wire leads explosive detonation. This report summarizes the underpinning technologies and physical processes that are currently understood and reviews the various efforts to quantify the mechanism by which the PETN is initiated. The behavior of the firing system is very well understood and predictable. The energy delivered to the wire has been empirically modelled but further investigation is required to understand the role of material heterogeneities and their effect on initiation. The energy delivered by the exploding wire has been quantified in many studies but it is not possible to correlate these to a particular design or firing regime and thus definitive conclusions are impossible. The energy absorbed by the PETN is also not well understood. Therefore, the initiation mechanism within the PETN EBWs has not been determined for EBW detonators. There is strong evidence that a shock-to-detonation (SDT) mechanism is not the sole cause of initiation. There is insufficient understanding of how electrical sparks transmit energy to PETN to make any judgement regarding the role gas ionization plays. Deflagration-to-detonation (DDT) seems like the most likely candidate for initiation but there is still a great lack of evidence for the presence of this mechanism.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

Proper orthogonal decomposition based reduced-order modeling of flux-Limited gray thermal radiation

Here, in this work, a proper orthogonal decomposition (POD) based reduced-order model (ROM) is developed to solve gray, flux-limited thermal radiation diffusion. We focus on the variable opacity radiation penetration benchmark posed by Olson, Auer, and Hall. The T -3 relationship for opacity in conjunction with high-temperature radiation penetrating an initially cold material produces a strong thermal radiation shock. This class of problems is particularly challenging for standard POD-based reduced-order modeling due to the nonlinearities presented by 1) the T 4 source term, and 2) flux-limited diffusion operator. To address these challenges and develop a cost competitive ROM, we employ a “hyper-reduction” technique through discrete empirical interpolation (DEIM) and allow for adaptive reduced-order projections through principal interval decomposition (PID). Performance of the proposed methodology is quantified by comparing the cost savings and accuracy relative to a full-order computation. Reference solutions and snapshot data are obtained through a full-order calculation performed by the University of Chicago maintained astrophysics code, FLASH. For consistency and potential extensibility, the developed ROM is also implemented in FLASH. We find that in the initialization regime, where the thermal radiation wave is initially created by the warming of the material, this class of problems is highly reducible and suitable for POD-based ROMs. However, the strong convective nature of the wave propagation regime is less reducible and more challenging to create an efficient ROM.

42 ENGINEERING↗

DOE OSTI2021

Magnetic Reconnection Inside Solar Wind Rotational Discontinuity During Its Interaction With the Quasi-Perpendicular Bow Shock and Magnetosheath

Here, using a three-dimensional global hybrid simulation, we investigate the formation and evolution of ion-scale magnetic reconnection inside an interplanetary rotational discontinuity (RD) owing to its interaction with the quasi-perpendicular (Q-⟂) bow shock and the magnetosphere. The interplanetary magnetic field (IMF) is initially predominantly northward, while it changes to purely southward across the RD. A significantly thinned RD current layer with a width ~ ion skin depth and normal magnetic field B n ≈0 is formed by a shock compression process as the RD interacts with the Q-⟂ shock. Magnetic reconnection thereupon takes place inside the thin RD current layer, where Hall magnetic and electric fields, reconnection electric field, and high-speed ion outflow jets are identified. Simultaneously, flux ropes form with an extension of a few ion inertial lengths. As the RD is transmitted into the magnetosheath, multiple reconnection sites lead to the formation of longer flux ropes. Moreover, magnetosheath reconnection is also found at new reconnection sites inside the RD. No reconnection is found in the Q-⟂ shock alone outside the RD. The flux ropes propagate poleward and tailward in the magnetosheath. In addition, magnetopause reconnection takes place under the southward IMF on the sunward side of the RD after the RD passes through the magnetopause.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Using limited neural networks to assess relative mechanistic influence on shock heating in granular solids

The rapid compaction of granular media results in localized heating that can induce chemical reactions, phase transformations, and melting. However, there are numerous mechanisms in play that can be dependent on a variety of microstructural features. Machine learning techniques such as neural networks offer a ubiquitous method to develop models for physical processes. Limiting what kind of microstructural information is used as an input and assessing normalized changes in network error, the relative importance of different mechanisms can be inferred. Here we utilize binned, initial density information as network inputs to predict local shock heating in a granular high explosive trained from large-scale molecular dynamics simulations. In this study, the spatial extent of the density field used in the network is altered to assess the importance and relevant length scales of the physical mechanisms in play, where different microstructural features result in different predictive capabilities.

36 MATERIALS SCIENCE↗

DOE OSTI2021

The collapse and three-dimensional explosion of three-dimensional massive-star supernova progenitor models

ABSTRACT The explosion outcome and diagnostics of core-collapse supernovae depend sensitively on the nature of the stellar progenitor, but most studies to date have focused exclusively on one-dimensional, spherically symmetric massive star progenitors. We present some of the first core-collapse supernovae simulations of three-dimensional massive star supernovae progenitors, a 12.5- and a 15-M⊙ model, evolved in three dimensions from collapse to bounce through explosion with the radiation-hydrodynamic code fornax. We compare the results using those starting from three-dimensional progenitors to three-dimensional simulations of spherically symmetric, one-dimensional progenitors of the same mass. We find that the models evolved in three dimensions during the final stages of massive star evolution are more prone to explosion. The turbulence arising in these multidimensional initial models serves as seed turbulence that promotes shock revival. Detection of gravitational waves and neutrinos signals could reveal signatures of pre-bounce turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Sensitivity Effects of Hollow Glass Micro-Balloon Doping on RDX-Based Explosives

Sensitivity to initiation is an important characteristic of high explosives. Many chemical and physical properties are fine-tuned to deliver an energetic material that behaves according to the user’s specifications exactly. In some cases, it is advantageous to study the effects that non energetic additives have on the performance of an explosive material. Following on the promising results obtained in other experiments, a study is conducted on the effects of hollow glass micro-balloons (bubbles, spheres), or HGMB, on a material’s sensitivity. Threshold test data is compared between several formulations of explosives. The control formulation is an RDX-based explosive with a non-energetic binder, and the test formulations are identical in composition, but with the addition of HGMB, up to 6% by volume. Safety testing of the new HGMB-doped explosive formulations is conducted to ensure they can be produced and handled safely prior to intentional detonation. This experiment utilizes an attenuation card of varying thicknesses between the initiator and the test article to attenuate the shock imparted, and a witness plate is analyzed for each test article to determine a GO or NO GO result. The data collected and the conclusions of this study affect how additives like HGMB are utilized in future explosive sensitivity threshold experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Impacts of Multidimensional Progenitor Perturbations on Core-collapse Supernova Explosions

Numerical studies of core-collapse supernovae have demonstrated the importance of nonradial motions in precollapse progenitors on the explosion outcome. We use the Chimera neutrino radiation hydrodynamics code running seven two-dimensional simulations of 15 M⊙ progenitors with different progenitor structures introduced by different one- and two-dimensional precollapse stellar evolution environments to examine the impacts of stellar structure and nonspherical motion in the precollapse progenitor on the development of explosions. We compare the explosion evolution of these models in terms of shock dynamics, diagnostic energy, neutrino heating, accretion, explosion geometry, nuclear abundances, and turbulent convection. We also analyze how stochastic variation impacts our simulations. Contrary to results reported in prior studies examining the impacts of multidimensional progenitors, we observe similar shock revival times and explosion development in our simulations despite differences in initial compositions and structures. We find no discernible impact from the accretion of nonradial perturbations from a multi-D progenitor onto the stalled shock in the revival and strength of explosion, as fully developed neutrino-driven convection behind the stalled shock is similar for all our models. For models with physically sourced noise in the iron core, a strong oscillation of the shock occurs after bounce and deflects infall laterally, and accelerates the saturation of the lateral turbulent kinetic energy. An examination of model stochasticity shows that any prior expected impacts on explosive outcome due to convection-related perturbations lie below the detectable threshold of numerical variation.

Chen, Chien-Hui [North Carolina State University]↗

DOE OSTI2021

Strongly Anisotropic Thermomechanical Response to Shock Wave Loading in Oriented Samples of the Triclinic Molecular Crystal 1,3,5-Triamino-2,4,6-trinitrobenzene

All-atom molecular dynamics (MD) simulations were used to study shock wave loading in oriented single crystals of the highly anisotropic triclinic molecular crystal 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). The crystal structure consists of planar hydrogen-bonded sheets of individually planar TATB molecules that stack into graphitic-like layers. Shocks were studied for seven systematically prepared crystal orientations with limiting cases that correspond to shock propagation exactly perpendicular and exactly parallel to the graphitic-like layers. The simulations were performed for initially defect-free crystals using a reverse-ballistic configuration that generates explicit, supported shocks. Final longitudinal stress components are between ≈8.5 and ≈10.5 GPa for the 1.0 km s –1 impact speed studied. Orientation-dependent properties are reported including shock speeds, stresses, temperatures, compression ratios, and local material strain rates. Spatiotemporal maps of the temperature, stress tensor, material flow, and molecular orientations reveal complicated processes that arise for specific shock directions. Furthermore, the results indicate that TATB shock response is highly sensitive to crystal orientation, with significant qualitative differences for the time evolution of the stress tensor and temperature, elastic/inelastic compression response, defect formation and growth, critical von Mises stress, and strain rates during shock rise that span nearly an order of magnitude. A variety of inelastic deformation mechanisms are identified, ranging from crumpling of graphitic-like layers to dislocation-mediated plasticity to intense shear strain localization. To our knowledge, these are the first systematic MD simulations and analysis of explicit shock wave propagation along nontrivial crystal directions in a triclinic molecular crystal.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Microscopy X-ray imaging enriched with small angle X-ray scattering for few nanometer resolution reveals shock waves and compression in intense short pulse laser irradiation of solids

Understanding how laser pulses compress solids into high-energy-density states requires diagnostics that simultaneously resolve macroscopic geometry and nanometer-scale structure. Here we present a combined X-ray imaging (XRM) and small-angle X-ray scattering (SAXS) approach that bridges this diagnostic gap. Using the Matter in Extreme Conditions end station at LCLS, we irradiated 25 μm copper wires with 45 fs, 0.9 J, 800 nm pulses at 3.5 × 10 19 W/cm 2 while probing with 8.2 keV XFEL pulses. XRM visualizes the evolution of ablation, compression, and inward-propagating fronts with ∼ 200 nm resolution, while SAXS quantifies their nanometer-scale sharpness via the time-resolved evolution of scattering streaks. The joint analysis reveals that an initially smooth compression steepens into a nanometer-sharp shock front after t sh ≈ (18 ± 3) ps, consistent with an analytical steepening model and hydrodynamic simulations. The front reaches a velocity of c sh ≈ 25 k m / s and a lateral width of several tens of microns, demonstrating direct observation of shock formation and decay at solid density for the first time with few-nanometer precision. This integrated XRM–SAXS method establishes a quantitative, multi-scale diagnostic of laser-driven shocks in dense plasmas relevant to inertial confinement fusion, warm dense matter, and planetary physics.

Kluge, Thomas [Helmholtz-Zentrum Dresden-Rossendor↗

DOE OSTI2025

Thermal shock resistance of lightweight cements developed for geothermal conditions

Cements are a critical component in well construction, as they act to prevent well fluid and gas escape, prevent corrosion of the casing, and strengthen the wellbore to prevent deformation. Under the high temperature/pressure conditions common in geothermal systems, the injection of cold water for energy production is expected to induce cyclic damage to the borehole cement through the rapid temperature fluctuations. These “thermal shocks” are expected to cause casing shrinkage, annulus formation, and cement tensile stresses. To understand the effect of cold water injection on the wellbore environment, a set of rock-cement-steel samples were created to simulate the structure of a geothermal well. Lightweight thermally-insulating cement blends were tested under thermal shock conditions in this study. In each test, the samples were pressurized to an effective pressure of ~3.5 MPa and placed at high temperatures. Thermal shocks were performed by injecting cold water (~10-15 °C) through the samples at a constant rate while keeping the samples at high temperatures until the sample temperature stopped decreasing and deformation ceased. Eight thermal shock tests were conducted with each sample – two at 100 °C and six at 200 °C. Post-tests analysis was then conducted by cutting open each sample to examine the damage in each component of the simulated wellbore. Experimental results suggest that all samples experienced similar degrees of axial and lateral contraction during cold water injection, but for the most part this contraction is recoverable when injection halts. Post-test analysis revealed that fly ash cenosphere pre-treatment had the best effect on improving thermal shock resistance in the cement blends. Thermomechanical modeling of likely stress paths experienced by the cements during heating/cooling cycles shows that elasto-plastic cement constitutive behavior results in most plastic strain occurring during the initial heating steps, with mostly elastic strain occurring during the thermal shock cycles. In conclusion, this agrees with experimental evidence, suggesting that cement damage from shocking occurs via other mechanisms such as chemical alteration, corrosion, and fatigue.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Fermi and Swift Observations of GRB 190114C: Tracing the Evolution of High-energy Emission from Prompt to Afterglow

We report on the observations of gamma-ray burst (GRB) 190114C by the Fermi Gamma-ray Space Telescope and the Neil Gehrels Swift Observatory . The prompt gamma-ray emission was detected by the Fermi GRB Monitor (GBM), the Fermi Large Area Telescope (LAT), and the Swift Burst Alert Telescope (BAT) and the long-lived afterglow emission was subsequently observed by the GBM, LAT, Swift X-ray Telescope (XRT), and Swift UV Optical Telescope. The early-time observations reveal multiple emission components that evolve independently, with a delayed power-law component that exhibits significant spectral attenuation above 40 MeV in the first few seconds of the burst. This power-law component transitions to a harder spectrum that is consistent with the afterglow emission observed by the XRT at later times. This afterglow component is clearly identifiable in the GBM and BAT light curves as a slowly fading emission component on which the rest of the prompt emission is superimposed. As a result, we are able to observe the transition from internal-shock- to external-shock-dominated emission. We find that the temporal and spectral evolution of the broadband afterglow emission can be well modeled as synchrotron emission from a forward shock propagating into a wind-like circumstellar environment. We estimate the initial bulk Lorentz factor using the observed high-energy spectral cutoff. Considering the onset of the afterglow component, we constrain the deceleration radius at which this forward shock begins to radiate in order to estimate the maximum synchrotron energy as a function of time. We find that even in the LAT energy range, there exist high-energy photons that are in tension with the theoretical maximum energy that can be achieved through synchrotron emission from a shock. These violations of the maximum synchrotron energy are further compounded by the detection of very high-energy (VHE) emission above 300 GeV by MAGIC concurrent with our observations. We conclude that the observations of VHE photons from GRB 190114C necessitates either an additional emission mechanism at very high energies that is hidden in the synchrotron component in the LAT energy range, an acceleration mechanism that imparts energy to the particles at a rate that is faster than the electron synchrotron energy-loss rate, or revisions of the fundamental assumptions used in estimating the maximum photon energy attainable through the synchrotron process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Geometry and dynamics of passive scalar structures in compressible turbulent mixing

We present a structure-based numerical analysis of passive scalar mixing in decaying homogeneous isotropic turbulence (DHIT) and shock-turbulence interaction canonical configurations. The analysis focuses on the temporal evolution of ensembles of passive scalar structures, initialized as spheres of different sizes relative to the Taylor microscale. An algorithm is introduced to track the evolution of each individual structure and the interactions with other structures in the ensemble, relating changes in the surface geometry and the underlying physical processes (turbulent transport, scalar dissipation, and shock compression). The tracking algorithm is applied to datasets from shock-capturing direct numerical simulations of DHIT, with Taylor microscale Reynolds number Re λ =40 and turbulence Mach number M t =0.2 ⁠, and STI cases in which the turbulence is processed by a shock wave at Mach numbers M = 1.5 and 3.0. Temporal surface convolution increases for initially larger structures, resulting in a higher probability of locally hyperbolic geometries where breakup into smaller structures occurs. Shock-induced deformation of the structures amplifies breakup processes, enhancing mixing, particularly for larger structures. Mixing enhancement by the shock is manifested as an amplification of the surface-averaged scalar gradient, which increases for initially larger structures. The alignment between the scalar gradient and the most extensional strain-rate eigendirection on the scalar isosurfaces also increases across the shock. Larger magnitudes of the scalar gradient and its alignment with the most compressive strain-rate eigendirection correlate with flatter surface regions. Shock-induced structure compression increases the area coverage of flat regions, where the amplification of scalar gradient is localized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗