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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θ m , and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θ mol . Here, the scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.

Buoyancy–drag↗
DOE OSTI2026

Experiments and simulations on the Richtmyer-Meshkov instability with a thin intermediate layer

Experiments and simulations of the Richtmyer-Meshkov instability (RMI) in two- and three-layer configurations are presented. The two-layer case utilizes a light-over-heavy configuration and consists of air as the light gas and sulfur hexafluoride (SF 6 ) as the heavy gas. The three-layer case utilizes a light-intermediate-heavy configuration, with helium (He) as the light gas, air as the intermediate gas, and SF 6 as the heavy gas. Statistically significant differences in the mixing layer width of the lower interface are not observed between the two cases. This differs from the experiments of Schalles et al., where a small, though statistically significant, difference in mixing layer growth was observed between the two- and three-layer cases with a nominally two-dimensional, single mode perturbation. Notably, the perturbations on the lower interface in the present work do not grow large enough to significantly interact with the upper interface during the duration of the experiments. In conclusion, this suggests that the differences in mixing layer growth observed by Schalles et al. may be due to interactions of the perturbations on one interface with the other interface rather than being inherent to the three-layer problem.

42 ENGINEERING↗
DOE OSTI2025

Further Development of the Tamped Richtmyer-Meshkov Instability Method and Application to Molybdenum Dynamic Strength Calibration and Tabulation

The high pressure and high strain rate dynamic strength of Mo is experimentally and computationally investigated in the 3–20 GPa stress, 50–600 C temperature, and 10 5 –10 6 /s strain rate regimes using a modified tamped Richtmyer-Meshkov instability (RMI) method. Modifications to the tamped RMI method include a method to determine loading states during strain, a new strength calibration function based on interface shape, and a robust uncertainty quantification method. These modifications improve fidelity of the tamped RMI method, allowing evaluation of the compensating effects of pressure hardening, strain rate hardening, strain hardening, and thermal softening. The new calibration function based on interface shape is not limited to sinusoidal corrugations and could be applied to additional interface shapes. Plate impact experiments are performed at Argonne National Laboratory’s Advanced Photon Source’s Dynamic Compression Sector operated by Washington State University (DCS), driving a planar shock front through a corrugated Mo-D 2 O or Mo-C 8 F 18 interface, forcing the corrugation to significantly deform. The extent of interfacial deformation, RMI growth, is experimentally observed using X-ray phase contrast imaging at the DCS. RMI jet lengths and jet shapes are extracted from the experimental radiographs, then used to calibrate numerical simulations performed with the Sandia National Laboratories (SNL) hydrocode CTH. Mo yield strength, Y, as a function of shock pressure, P, strain rate, $\dot{\varepsilon }$, accumulated strain, ϵ, relative volumetric compression, RD , and temperature, T , is determined for each impact experiment and presented. The calibrated Mo yield strength values range 1.2–1.8 GPa, with strength generally decreasing as the impact stress increases. This trend is likely caused by thermal softening or strain localization. The tabular yield strength versus loading condition data presented in this paper can be used to fit complex strength models.

Voorhees, T. J. [Sandia National Lab. (SNL-CA), Li↗
DOE OSTI2025

Shock tube simulations for the three-layer Richtmyer–Meshkov instability with single-mode and multimode perturbations

While the canonical two-component, single-mode Richtmyer–Meshkov instability (RMI) has been extensively studied, relatively less work has focused on the effects of an additional intermediate-density middle layer. This work investigates such three-material RMI configurations at two Atwood number scenarios using the ARES hydrodynamics code. After validation against previous experimental and computational studies, setups corresponding to recent three-layer shock tube experiments are simulated. Cases with both single-mode and multimode perturbations are studied to quantify mixing across the interface between the materials with highest and intermediate density. In particular, this work is able to comprehensibly examine differences between two- and three-dimensional setups for the single-mode and multimode problems. Observations from previous two-layer investigations still apply in the three-layer setup, but over the time horizons considered, there appears to be insufficient nonlinear mode coupling to create significant differences between two- and three-dimensional simulations following the first passage of a shock. Finally, additional reshock simulations have additional nonlinear growth that does result in expected differences between two- and three-dimensional cases in this three-layer setup, but significant differences do not manifest during the time horizon studied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Passive Freeze-Out of the Richtmyer-Meshkov Instability

The Richtmyer-Meshkov instability (RMI) poses a major challenge in inertial confinement fusion (ICF) due to its role in mixing and performance degradation. We report the first experimental observation of passive freeze-out of RMI in a low-pressure surrogate regime, an instability stagnation effect induced without modifying the driving pressure pulse or the target surface geometry. Using additively manufactured subsurface voids in a sinusoidal target, we convert a single shock into a sequence of weaker shocks that suppress instability growth upstream of the surface by over 70%. High-speed x-ray imaging and hydrodynamic simulations suggest that this suppression arises primarily from temporal shaping, with lesser contributions from spatial curvature and shock weakening. Our results demonstrate a driver-independent pathway for controlling shock-driven hydrodynamic instabilities relevant to ICF and other high energy density systems.

Materials science↗
DOE OSTI2025

Low viscosity of solid MgO at high pressures and strain rates measured using the laser-driven Richtmyer-Meshkov instability

Solids are often assumed to behave as viscous fluids under high-strain rates. This behavior has been studied experimentally in metals but largely unexplored in brittle ceramic materials. Here, in this study, we present a technique for measuring the viscosity of MgO using time-resolved velocimetry to track the growth rate of a perturbation caused by the Richtmyer-Meshkov instability at the OMEGA EP laser facility. To interpret the results, we use an in-house Eulerian hydrocode to simulate our experiments and model the plastic deformation of solid MgO as a viscous fluid. Results indicate that MgO has a surprisingly low upper bound to its effective viscosity of ∼10 2 ⁢ Pa s at 175 ± 15⁢ GPa, ∼3500⁢K, and 10 6 −10 7 s −1 strain rate.

Perez, Tyler M. [Johns Hopkins Univ., Baltimore, M↗
DOE OSTI2025

Differentiable lagrangian shock hydrodynamics with application to stable shock acceleration of density interfaces

We develop a gradient based optimization approach for the equations of compressible, Lagrangian hydrodynamics and demonstrate how it can be employed to automatically uncover strategies to control hydrodynamic instabilities arising from shock acceleration of density interfaces. Strategies for controlling the Richtmyer-Meshkov instability (RMI) are of great benefit for inertial confinement fusion (ICF) where shock interactions with many small imperfections in the density interface lead to instabilities which rapidly grow over time. These instabilities lead to mixing which, in the case of laser driven ICF, quenches the runaway fusion process ruining the potential for positive energy return. Here, we demonstrate that control of these instabilities can be achieved by optimization of initial conditions with ( > 100) parameters. Optimizing over a large parameter space like this is not possible with gradient-free optimization strategies. This requires computation of the gradient of the outputs of a numerical solution to the equations of Lagrangian hydrodynamics with respect to the inputs. We show that the efficient computation of these gradients is made possible via a judicious application of (i) adjoint methods, the exact formal representation of sensitivities involving partial differential equations, and (ii) automatic differentiation (AD), the algorithmic calculation of derivatives of functions. Careful regularization of multiple operators including artificial viscosity and timestep control is required. We perform design optimization of > 100 parameter energy field driving the Richtmyer Meshkov instability showing significant suppression while simultaneously enhancing the acceleration of the interface relative to a nominal baseline case.

Hydrophysics↗
DOE OSTI2025

Dynamic Strength and Equation of State of Epon 828 and Diethanolamine (DEA) Polymer Epoxy Under Shock Loading

Polymers are increasingly utilized in engineering applications that can experience high loading rates, necessitating increased understanding of their response under such conditions. The tamped Richtmyer-Meshkov Instability (RMI) method was used to characterize the equation of state and dynamic strength of the polymer Epon 828 cured with Diethanolamine (DEA). Plate impact experiments that drove a uniaxial shock compression wave across a sinusoidally corrugated metal-polymer interface were performed to generate shock stresses from 4-12 GPa and strain rates of approximately 1/s in the polymer. X-ray phase contrast imaging recorded the shock motion in the polymer and subsequent interface evolution. Analysis of this data yielded the polymer equation of state and, in conjunction with numerical modeling, the dynamic strength. The equation of state was validated against one-dimensional plate impact experiments from existing literature. The dynamic strength was compared to prior data for Epon 828 and related polymers at lower strain rates and found to exhibit significant strain rate and pressure-hardening effects. The strength of the Epon 828 polymer at 10 6 1/s was found to be approximately 1.5 GPa, suggesting that it is comparable to the strength of high strength metals at these dynamic conditions.

Equation of state↗
DOE OSTI2025

Experimental platforms for investigating feature-driven jets for HED mix model validation

High-energy-density (HED) systems, such as inertial confinement fusion (ICF), are susceptible to hydrodynamic instabilities that can significantly affect both experimental results and modeling predictions. Isolated features, such as fill tubes or divots in the capsule, can cause material to jet as a result of the compressive shock exciting the Richtmyer–Meshkov instability, and serve as one of the primary degradation mechanisms in ICF yield. Simulations of feature-driven jets and how they mix require extensive experimental validation, particularly for understanding to what degree the initial size and shape of a feature influence jet dynamics, and how much instability feeds through downstream layers. A better understanding of feature-driven jetting can improve our mix modeling capabilities and increase hydrodynamic simulation accuracy. This manuscript describes a series of experimental platforms fielded by Los Alamos National Laboratory as a part of the Mshock Omega 60 and ModCons Omega EP campaigns to explore feature-driven jetting. These platforms are designed to benchmark jet evolution and growth as a function of initial feature size and shape, investigate jet-layer interactions leading to instability feedthrough, and will be used to characterize jet-jet interactions resulting from clusters of features. In conclusion, preliminary results for both platforms are shown. The ModCons experiments are on-going, and a discussion of future work directions is included.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Generalizing the compressible pairwise interaction extended point-particle model

Ejecta physics plays an important role in material interfaces that are impacted by a strong shock wave. When a shock impacts a rough surface of solid material and melts it, the Richtmyer–Meshkov instability grows perturbations on the surface, which can eject particles. After release, the ejecta travel through the post-shock compressible flow. To accurately simulate a large number of ejecta particles, an Euler–Lagrange approach is preferred, which requires modeling the subgrid-scale physics involved with fluid–particle interactions. We generalize the previous work from Hsiao et al. (2023) to consider systems of moving particles subject to any loading shock. The following improvements were made: (1) Particles are allowed to move relative to each other (2) Non-planar shocks are accounted for along with allowing for variable shock speeds. As a result, the generalized algorithm was tested with particle-resolved simulations for canonical test cases. The results of these tests are discussed and analyzed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Shock-induced bubble jets: a dual perspective of bubble collapse and interfacial instability theory

Interactions between shock waves and gas bubbles in a liquid can lead to bubble collapse and high-speed liquid jet formation, relevant to biomedical applications such as shock wave lithotripsy and targeted drug delivery. This study reveals a complex interplay between acceleration-induced instabilities that drive jet formation and radial accelerations causing overall bubble collapse under shock wave pressure. Using high-speed synchrotron X-ray phase contrast imaging, the dynamics of micrometre-sized air bubbles interacting with laser-induced underwater shock waves are visualised. These images offer full optical access to phase discontinuities along the X-ray path, including jet formation, its propagation inside the bubble, and penetration through the distal side. Jet formation from laser-induced shock waves is suggested to be an acceleration-driven process. A model predicting jet speed based on the perturbation growth rate of a single-mode Richtmyer–Meshkov instability shows good agreement with experimental data, despite uncertainties in the jet-driving mechanisms. The jet initially follows a linear growth phase, transitioning into a nonlinear regime as it evolves. To capture this transition, a heuristic model bridging the linear and nonlinear growth phases is introduced, also approximating jet shape as a single-mode instability, again matching experimental observations. Upon piercing the distal bubble surface, jets can entrain gas and form a toroidal secondary bubble. Linear scaling laws are identified for the pinch-off time and volume of the ejected bubble relative to the jet’s Weber number, characterising the balance of inertia and surface tension. At low speeds, jets destabilise due to capillary effects, resulting in ligament pinch-off.

Drops and Bubbles: Bubble dynamics↗
DOE OSTI2024

Equation-of-state measured via x-ray phase contrast imaging for Epon 828/DEA epoxy

Epoxies are a broad class of polymer materials often used as adhesive, structural or binding materials. Epon 828 is an epoxy resin that can be polymerized with a variety of curing agents with the choice of curing agent potentially having an effect on the resulting epoxy polymer’s material properties. In this study, the dynamic behavior of Epon 828 epoxy resin cured with diethanolamine (DEA) is investigated through a series of tamped Richtmyer-Meshkov instability (RMI) experiments measured with x-ray phase-contrast imaging. The measured shock and particle velocities are combined with data in the literature to calibrate Mie-Grüneisen equations-of-state (EOS) for portions and combinations of the collective dataset. The calibrated Mie-Grüneisen EOS are validated against particle velocity profiles extracted from published literature using the Eulerian hydrocode CTH. Here, the Mie-Grüneisen EOS fit to only the tamped RMI experimental data presented here most closely follows the particle velocity profile in the published literature.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A point-particle-based hydride shell-shedding model for ejecta particle transport in reactive environments

A shock wave passing over a rough or perturbed metal surface will induce a limiting case of Richtmyer–Meshkov instability and will cause small particles to eject from the surface and transport into the surrounding medium. These particles are known as ejecta and can be either solid or liquid in nature. Recent experiments have shown that liquid cerium ejecta clouds exhibit unexpected non-monotonic acceleration behaviors as well as temperature plateaus after a brief temperature rise if they are transporting in a chemically reactive, hydrogen-based medium while they act as expected in an inert medium. This work details a point-particle model developed for reactive cerium ejecta transport, which attempts to account for these new physics through the behavior of a developing solid hydride shell, which is believed to form as a product of the reaction. The overall model incorporates the effects of the reaction on the particle properties as well as the effects of potential shedding of the shell into sub-micrometer scale flakes and potential phase change of the hydride if the ejecta particles reach the melt point of the hydride layer. The model is tested by performing simulations of the original motivating experiments and comparing quantities, such as ejected mass, velocimetry, and temperature profiles, against the experimental data. While the model is able to capture many general features of the observed anomalies, some inaccuracies still exist. These point to both missing physics in the model (such as a deuterium adsorption mechanism on the hydride layer) as well as a lack of knowledge of certain material properties (such as the strength of cerium hydride to determine dynamic fracture thicknesses) needed to fully reduce the uncertainties in the model by up to an order of magnitude and perform a true attempt at model validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A stress-based fracture model for reacting metal ejecta

The evolution of reacting metal ejecta continues to be a topic of interest at the forefront of metals in reactive and extreme environments. Ejecta are small particles formed when the surface of a metal undergoes Richtmyer–Meshkov instability from a strong shock. Experiments have shown that in the case where ejecta are in ambient conditions that induce a reaction, the ejecta behave irregularly. The ejecta temperature rises and then plateaus, and the acceleration profile shows unexpected jumps. These variations are assumed to be related to the exothermic heat release and particle mass loss caused by the reaction. To explain this phenomenon, efforts to model this in simulations have increased. While current models can capture many of these physical processes, they currently assign a constant reaction shell thickness with little physical reasoning. This work remedies this problem by assigning a dynamic physically informed shell thickness to the reacting particles, using solid analysis. The shell thickness of the particles impacts the rate of change of reacted mass in the system, as well as the rate at which the particles react. The model is based on a simple stress–strain relationship and gives a dynamic assignment for when the reacting particle should begin to fracture. We compare our model to the previous computational and simulation data to analyze the effects of different model parameters.

42 ENGINEERING↗
DOE OSTI2026

Influence of the drive design on ablation front hydrodynamic instability growth in a capsule implosion at the National Ignition Facility

A critical aspect of inertial confinement fusion experiments lies in the control of ablation front instabilities during the implosion process. The growth of Rayleigh–Taylor and Richtmyer–Meshkov instabilities, seeded by target defects, can significantly degrade the performance of the implosion. Here, this study explores the influence of drive design on ablation front stability using the hydro-growth radiography platform at the National Ignition Facility. This platform allows the measurement of the ablation front hydrodynamic instability growth. Because these measurements are restricted to early convergence, their primary role is to constrain the initial instability growth and benchmark the simulations used to infer shell integrity and performance at peak velocity and ignition. Three ignition designs, Hybrid-E (HyE), SQ-n (“S” for scaling and “Q” for quality), and High temperature, High thickness (HiT) were analyzed. The results demonstrated a high dependence of the growth factor on the choice of design, capsule scale as well as the hohlraum conditions, mainly the radiative temperature and the gold M-band emission. HyE and SQ-n display a similar growth factor range, but their evolution is different due to the design differences in hohlraum conditions. HiT has the lowest growth factor of the studied designs, which is a result of a higher radiative temperature. These results highlight the importance of design choices in controlling instability dynamics. These insights inform future drive design strategies to enhance stability and efficiency in fusion ignition experiments.

Physics↗
DOE OSTI2026

Vanishing dynamic strength measured in a transient high-pressure phase of tin

This work reports two independent experimental estimations of the dynamic strength of the body-centered tetragonal (bct) 𝛾 phase of tin, which occurs at pressures above about 9 GPa and transforms promptly back to the ambient 𝛽 phase upon pressure release. Measuring strength in such a transient high-pressure phase is challenging. One measurement used free-surface Richtmyer-Meshkov instabilities generated with gas gun impact. Another set of measurements used ramp-release loading in a pulsed-power facility. Strength estimations came from comparison to simulations using a comprehensive multiphase modeling framework that includes equation of state, shear moduli, and strength separately for each phase, and treats mixed-phase regions. Both experimental methods found the 𝛾-phase strength to be very low, within experimental uncertainty of zero. The existing literature on other materials, by contrast, almost universally reports higher strength in transient high-pressure phases compared with ambient phases. Recent Molecular-Dynamics simulations on tin in the literature showed almost zero deviatoric strength during a deformation-induced bct → bct transformation in which one of the 𝛾-phase 𝑎 axes “flips” to the 𝑐 axis. This reorientation currently provides the most plausible explanation for the low observed strength in 𝛾-phase tin.

36 MATERIALS SCIENCE↗