Abstract: Self-heating thermionic hollow cathodes are essential components in modern plasma thrusters. To fully understand their operation, three interdependent physical domains must be considered: plasma discharge physics, thermal response of the cathode structure, and chemical evolution of plasma exposed surfaces. In this work, we develop the first self-consistently coupled plasma–thermal–chemical simulation platform for hollow cathode operation using lanthanum hexaboride (LaB₆) and Xe and study its performance against our experimentally determined temperature measurements. Results show that the customary assumptions of single-step resonant neutralization and full energy accommodation in ion-surface collisions fail to reproduce our empirical observations. We propose a two-step neutralization mechanism that consists of resonant neutralization to the first excited state of xenon followed by Auger de-excitation to the ground state, along with system specific accommodation factors. In this way, the agreement between the results of the simulations and experiments was achieved. These fundamental processes could govern neutralization in other cathode technologies where low work function emitters are employed and should therefore be accounted for in physical models. In addition, the new simulation platform allows us to better estimate the equilibrium work function of LaB₆ hollow cathode emitters. In the cathode studied here, we found that the effective work function is 2.25 eV, which is significantly lower than previous estimates, and leads to better than expected cathode material performance with important implications for space missions.

Publication: Journal of Applied Physics Vol.: 130 No.: 4 ISSN: 0021-8979

ID: CaltechAUTHORS:20210927-225706896

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Abstract: In his 1932 address to the British Society for the Advancement of Science the famed mathematician Sir Horace Lamb was said to have made the following seemingly prescient statement: ‘I am an old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. About the former, I am really rather optimistic’. Turbulent flow is a ubiquitous aspect of nature and its understanding has important implications for a wide variety of applications including weather prediction, industrial flows and aeronautics. Increasingly detailed and precise experiments combined with highly resolved numerical simulations have led to some insights, but despite over 100 years of research a full understanding of the detailed mechanics of turbulence and its implications for quantities of applied interest such as drag, lift and mixture fraction remains incomplete. For example, as understood by G. I. Taylor, an important goal is to predict the statistics of a turbulent flow. Even under simplifying assumptions that the statistics are homogeneous (i.e. invariant under translation) and isotropic, we still do not have satisfactory theories for the formation and maintenance under large scale forcing of the so-called inertial range Kolmogorov energy spectrum. We have a lot of what Philip Saffman termed ‘postdictions’ but very few real predictions. Homogeneous isotropic turbulence is an idealization and in real flows one must contend also with sources of anisotropy such as rotation, stratification or shear, as well as inhomogeneity arising from geometry as occurs for example in boundary layers. Nevertheless, there has been important progress in all areas.

Publication: Journal of Fluid Mechanics Vol.: 864ISSN: 0022-1120

ID: CaltechAUTHORS:20190624-081641159

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Abstract: High resolution large eddy simulations (LES) are performed to study the interaction of a stationary shock with fully developed turbulent flow. Turbulent statistics downstream of the interaction are provided for a range of weakly compressible upstream turbulent Mach numbers M_t = 0.03−0.18, shock Mach numbers M_s = 1.2−3.0 and Taylor-based Reynolds numbers Re_λ = 20−2500. The LES displays minimal Reynolds number effects once an inertial range has developed for Re_λ > 100. The inertial range scales of the turbulence are shown to quickly return to isotropy, and downstream of sufficiently strong shocks this process generates a net transfer of energy from transverse into streamwise velocity fluctuations. The streamwise shock displacements are shown to approximately follow a k^(−11/3) decay with wavenumber as predicted by linear analysis. In conjunction with other statistics this suggests that the instantaneous interaction of the shock with the upstream turbulence proceeds in an approximately linear manner, but nonlinear effects immediately downstream of the shock significantly modify the flow even at the lowest considered turbulent Mach numbers.

Publication: Journal of Fluid Mechanics Vol.: 858ISSN: 0022-1120

ID: CaltechAUTHORS:20181120-151734295

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Abstract: Self-heating hollow cathodes are central components in modern electric thrusters. The plasma discharge inside these devices heats the internal components, thus maintaining the temperatures required for electron emission. Precise knowledge of the physical phenomena governing hollow cathode operation is key to predict their lifetime, specifically, their thermionic emission characteristics. A simulation platform has been built to couple plasma and thermal models of the self-heating hollow cathode to produce a self-consistent solution. A self-consistent solution has been found for a LaB_6 hollow cathode operating at 25A and 13 sccm where the work function is assumed to be spatially uniform along the emitter with a value which is allowed to vary as the coupled model iterates to a self-consistent solution. The emitter temperature from the converged solution does not agree with experimental temperature measurements, however. The results of a sensitivity analysis suggest that none of the tolerances in the measurement are responsible for the discrepancy. We hypothesize that either the work function needs to be a function of position along the emitting surfaces or the heat fluxes have been overestimated in the plasma solver.

ID: CaltechAUTHORS:20190805-134838581

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Abstract: The rapid change in scales over a shock has the potential to introduce unique difficulties in Large Eddy Simulations (LES) of compressible shock-turbulence flows if the governing model does not sufficiently capture the spectral distribution of energy in the upstream turbulence. A method for the regularization of LES of shock-turbulence interactions is presented which is constructed to enforce that the energy content in the highest resolved wavenumbers decays as k^(−5/3), and is computed locally in physical-space at low computational cost. The application of the regularization to an existing subgrid scale model is shown to remove high wavenumber errors while maintaining agreement with Direct Numerical Simulations (DNS) of forced and decaying isotropic turbulence. Linear interaction analysis is implemented to model the interaction of a shock with isotropic turbulence from LES. Comparisons to analytical models suggest that the regularization significantly improves the ability of the LES to predict amplifications in subgrid terms over the modeled shockwave. LES and DNS of decaying, modeled post shock turbulence are also considered, and inclusion of the regularization in shock-turbulence LES is shown to improve agreement with lower Reynolds number DNS.

Publication: Journal of Computational Physics Vol.: 361ISSN: 0021-9991

ID: CaltechAUTHORS:20180214-082550535

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Abstract: We present a detailed study of the interface instability that develops at the boundary between a shell of elastic–plastic material and a cylindrical core of confined gas during the inbound implosive motion generated by a shock-wave. The main instability in this configuration is the so-called Richtmyer–Meshkov instability that arises when the shock wave crosses the material interface. Secondary instabilities, such as Rayleigh–Taylor, due to the acceleration of the interface, and Kelvin–Helmholtz, due to slip between solid and fluid, arise as the motion progresses. The reflection of the shock wave at the axis and its second interaction with the material interface as the shock moves outbound, commonly known as re-shock, results in a second Richtmyer–Meshkov instability that potentially increases the growth rate of interface perturbations, resulting in the formation of a mixing zone typical of fluid–fluid configurations and the loss of the initial perturbation length scales. The study of this problem is of interest for achieving stable inertial confinement fusion reactions but its complexity and the material conditions produced by the implosion close to the axis prove to be challenging for both experimental and numerical approaches. In this paper, we attempt to circumvent some of the difficulties associated with a classical numerical treatment of this problem, such as element inversion in Lagrangian methods or failure to maintain the relationship between the determinant of the deformation tensor and the density in Eulerian approaches, and to provide a description of the different events that occur during the motion of the interface. For this purpose, a multi-material numerical solver for evolving in time the equations of motion for solid and fluid media in an Eulerian formalism has been implemented in a Cartesian grid. Equations of state are derived using thermodynamically consistent hyperelastic relations between internal energy and stresses. The resolution required for capturing the state of solid and fluid materials close to the origin is achieved by making use of adaptive mesh refinement techniques. Rigid-body rotations contained in the deformation tensor have been shown to have a negative effect on the accuracy of the method in extreme compression conditions and are removed by transforming the deformation tensor into a stretch tensor at each time step. With this methodology, the evolution of the interface can be tracked up to a point at which numerical convergence cannot be achieved due to the inception of numerical Kelvin–Helmholtz instabilities caused by slip between materials. From that point, only qualitative conclusions can be extracted from this analysis. The influence of different geometrical parameters, initial conditions, and material properties on the motion of the interface are investigated. Some major differences are found with respect to the better understood fluid–fluid case. For example, increasing the wave number of the interface perturbations leads to a second phase reversal of the interface (i.e., the first phase reversal of the interface naturally occurs due to the initial negative growth-rate of the instability as the shock wave transitions from the high-density material to the low-density one). This phenomenon is caused by the compressive effect of the converging geometry and the low density of the gas with respect to the solid, which allows for the formation of an incipient spike in the center of an already existing bubble. Multiple solid–gas density ratios are also considered. Results show that the motion of the interface asymptotically converges to the solid–vacuum case. When a higher initial density for the gas is considered, the growth rate of interface perturbations decreases and, in some situations, its sign may reverse, as the fluid becomes more dense than the solid due to having higher compressibility. Finally, the influence of the Mach number of the driving shock and the yield stress on the mixing-zone is examined. We find that the width of the mixing zone produced after the re-shock increases in proportion to the strength of the incident shock. An increased yield stress in the solid material makes the interface less unstable due to vorticity being carried away from the interface by shear waves and limits the generation of smaller length scales after the re-shock.

Publication: Journal of the Mechanics and Physics of Solids Vol.: 76ISSN: 0022-5096

ID: CaltechAUTHORS:20150403-130428593

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Abstract: The impact of a shock-wave onto a perturbed interface separating materials of different density and initially at rest in a laboratory frame of reference is described as a Richtmer-Meshkov (RM) flow, following Richtmyer [1], who obtained a numerical solution to the linearized equations for perfect fluids using an impulsive model, and Meshkov [2], who performed shock-tube experiments for gaseous materials.

Vol.: 2
ID: CaltechAUTHORS:20170621-144124277

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Abstract: We present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ≈1.2, the density ratio (precisely |A_0|≈0.67) and the perturbation shape (dominant spherical wavenumber ℓ_0=40 and amplitude-to-initial radius of 3%): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. Turbulent statistics are developed in Part 2 (Lombardini, M., Pullin, D. I. & Meiron, D. I. J. Fluid Mech., vol. 748, 2014, pp. 113–142). A wave-diagram analysis of the radially symmetric flow highlights that the light–heavy mixing layer is processed by consecutive reshocks, and not by reverberating rarefaction waves as is usually observed in planar geometry. Less surprisingly, reshocks process the heavy–light mixing layer as in the planar case. In both configurations, the incident imploding shock and the reshocks induce Richtmyer–Meshkov (RM) instabilities at the density layer. However, we observe differences in the mixing-layer growth because the RM instability occurrences, Rayleigh–Taylor (RT) unstable scenarios (due to the radially accelerated motion of the layer) and phase inversion events are different. A small-amplitude stability analysis along the lines of Bell (Los Alamos Scientific Laboratory Report, LA-1321, 1951) and Plesset (J. Appl. Phys., vol. 25, 1954, pp. 96–98) helps quantify the effects of the mean flow on the mixing-layer growth by decoupling the effects of RT/RM instabilities from Bell–Plesset effects associated with geometric convergence and compressibility for arbitrary convergence ratios. The analysis indicates that baroclinic instabilities are the dominant effect, considering the low convergence ratio (≈2) and rather high (ℓ>10) mode numbers considered.

Publication: Journal of Fluid Mechanics Vol.: 748ISSN: 0022-1120

ID: CaltechAUTHORS:20140708-095145766

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Abstract: We present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ≈ 1.2, the density ratio (precisely |A_0| ≈ 0.67) and the perturbation shape (dominant spherical wavenumber ℓ_0=40 and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85-112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios ≈2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter Theta and the effective Atwood ratio A(e), which reach similar late time values in both light-heavy and heavy-light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated ≈2000 in the light-heavy case and 1000 in the heavy-light case. An analysis of the density self-correlation b, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh-Taylor (RT) turbulence. These traits are more pronounced in the light-heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light-heavy from heavy-light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy-light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer-Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like -5/3 power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

Publication: Journal of Fluid Mechanics Vol.: 748ISSN: 0022-1120

ID: CaltechAUTHORS:20140708-150458718

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Abstract: The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum (heavy-light configuration) is studied by means of computational techniques. A fully Eulerian multimaterial algorithm that solves consistently the Euler equations and the time evolution of the deformations in the material is applied to three distinct materials (copper, aluminum, and stainless steel). If a perfectly plastic constitutive relation is considered, an empirical law is computed that relates the long-term perturbation amplitude of the interface, its maximum growth rate, the initial density, and the yield stress of the material. It is shown that this linear relation can be extended to materials that follow more complex plastic behavior which can account for rate dependency, hardening, and thermal softening, and to situations in which small-perturbation theory is no longer valid. In effect, the yield stress computed from measurements of the long-term amplitude and maximum growth rate closely matches the von Mises stress found at the interface of solid materials for a wide range of cases with different initial parameters.

Publication: Physical Review E Vol.: 89 No.: 3 ISSN: 1539-3755

ID: CaltechAUTHORS:20140501-094156957

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Abstract: An Eulerian, multi-material numerical method is described for computing dynamic problems involving large deformations in elastic–plastic solids. This approach addresses algorithm failures associated with reconnection and change in topology observed in previously proposed formulations. Among the information contained in the deformation gradients commonly employed for defining constitutive laws suitable for solids, only the symmetric matrix tensor obtained from a polar decomposition of the elastic component of the deformation is required to determine the stress state. The numerical utilization of this symmetric tensor, associated with material stretch, eliminates undesirable, discontinuous deformation states produced by local rigid-body rotations at same-material reconnecting interfaces. Such states appear even where stress states in impacting regions are similar. The temporal evolution of the stretches neither modifies the eigenstructure of the system of equations nor changes its size. We also present a new multi-material approximate Riemann solver based on the HLLD approach, previously applied to other hyperbolic systems, in which waves of distinct velocity exist, for example, as in magnetohydrodynamics. This solver is employed in combination with the modified ghost fluid method (M-GFM) in the description of multi-material interfaces. These composite algorithms enable numerical simulations of the Richtmyer–Meshkov instability (i.e., the instability produced by the interaction of an interface separating materials of different density with a shock wave at an angle) in converging geometries for solid materials that would have previously led to the failure of the method.

Publication: Journal of Computational Physics Vol.: 257ISSN: 0021-9991

ID: CaltechAUTHORS:20131223-152813111

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Abstract: Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell’s model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

Publication: Journal of Computational Physics Vol.: 240ISSN: 0021-9991

ID: CaltechAUTHORS:20130506-071017370

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Abstract: This article surveys the contributions of Philip Geoffrey Saffman to our knowledge of fluid-dynamical phenomena both in nature and in the laboratory. We begin with Saffman’s first work on fluid mechanics in Cambridge, England, in the mid-1950s and then describe the evolution of his ideas and research, over many diverse areas in fluid mechanics until his final paper in 2002. It is argued that Saffman brought a unique perspective to our interpretation of fluid mechanics as a broad scientific discipline that remains with us today.

Publication: Annual Review of Fluid Mechanics Vol.: 45ISSN: 0066-4189

ID: CaltechAUTHORS:20130503-085656140

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Abstract: Large-eddy simulations of single-shock-driven mixing suggest that, for sufficiently high incident Mach numbers, a two-gas mixing layer ultimately evolves to a late-time, fully developed turbulent flow, with Kolmogorov-like inertial subrange following a -5/3 power law. After estimating the kinetic energy injected into the diffuse density layer during the initial shock–interface interaction, we propose a semi-empirical characterization of fully developed turbulence in such flows, based on scale separation, as a function of the initial parameter space, as (η_(0^+)Δu/ν)(η_(0^+)/L_ρ)A^+/√(1-A^(+)^2) ≳ 1.53 × 10^4/C^2, which corresponds to late-time Taylor-scale Reynolds numbers ≳250. In this expression, η_(0^+) represents the post-shock perturbation amplitude, Δu the change in interface velocity induced by the shock refraction, ν the characteristic kinematic viscosity of the mixture, L_ρ the inner diffuse thickness of the initial density profile, A^+ the post-shock Atwood ratio, and C(A^+, η_(0^+)/λ_0)≈0.3 for the gas combination and post-shock perturbation amplitude considered. The initially perturbed interface separating air and SF_6 (pre-shock Atwood ratio A ≈ 0.67) was impacted in a heavy–light configuration by a shock wave of Mach number M_I = 1.05, 1.25, 1.56, 3.0 or 5.0, for which η_(0^+) is fixed at about 25% of the dominant wavelength λ_0 of an initial, Gaussian perturbation spectrum. Only partial isotropization of the flow (in the sense of turbulent kinetic energy and dissipation) is observed during the late-time evolution of the mixing zone. For all Mach numbers considered, the late-time flow resembles homogeneous decaying turbulence of Batchelor type, with a turbulent kinetic energy decay exponent n ≈ 1.4 and large-scale (k⟶0) energy spectrum ~k^4, and a molecular mixing fraction parameter, Θ ≈ 0.85. An appropriate time scale characterizing the Taylor-scale Reynolds number decay, as well as the evolution of mixing parameters such as Θ and the effective Atwood ratio A_e, seem to indicate the existence of low- and high-Mach-number regimes.

Publication: Journal of Fluid Mechanics Vol.: 690ISSN: 0022-1120

ID: CaltechAUTHORS:20120227-122525364

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Abstract: The study of cylindrical and spherical converging shock waves propagating in solid materials is relevant to the production of high temperatures and pressures in condensed matter with applications to inertial confinement fusion [1]. However, experimental studies conducted in the area are prone to complications derived from the measurement techniques available and the difficulty of producing a quasi-radially symmetric flow.

Vol.: 2
ID: CaltechAUTHORS:20200520-110119540

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Abstract: We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate.

Publication: Journal of Fluid Mechanics Vol.: 670ISSN: 0022-1120

ID: CaltechAUTHORS:20110323-142306126

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Abstract: We present a finite-difference based solver for hyper-elastic and viscoplastic systems using a hybrid of the weighted essentially non-oscillatory (WENO) schemes combined with explicit centered difference to solve the equations of motion expressed in an Eulerian formulation. By construction our approach minimizes both numerical dissipation errors and the creation of curl-constraint violating errors away from discontinuities while avoiding the calculation of hyperbolic characteristics often needed in general finite-volume schemes. As a result of the latter feature, the formulation allows for a wide range of constitutive relations and only an upper-bound on the speed of sound at each time is required to ensure a stable timestep is chosen. Several one- and two-dimensional examples are presented using a range of constitutive laws with and without additional plastic modeling. In addition we extend the reflection technique combined with ghost-cells to enforce fixed boundaries with a zero tangential stress condition (i.e. free-slip).

Publication: Journal of Computational Physics Vol.: 229 No.: 24 ISSN: 0021-9991

ID: CaltechAUTHORS:20110302-102610242

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Abstract: We present an analytical study of the linearized impulsive Richtmyer-Meshkov flow for incompressible elastic solids. Seminumerical prior investigations of a related shock-driven compressible elastic problem suggest that the interface amplitude remains bounded in time, in contrast to the unstable behavior found for gases. Our approach considers a base unperturbed flow and a linearization of the conservation equations around the base solution. The resulting initial and boundary value problem is solved using Laplace transform techniques. Analysis of the singularities of the resultant function in the Laplace domain allows us to perform a parametric study of the behavior of the interface in time. We identify two differentiated long-term patterns for the interface, which depends on the material properties: standing wave and oscillating decay. Finally, we present results for the vorticity distribution, which show that the shear stiffness of the solids is responsible both for the stabilization of the interface, and also for the period of the interface oscillations. Comparisons with previous results are discussed.

Publication: Physical Review E Vol.: 81 No.: 6 ISSN: 1539-3755

ID: CaltechAUTHORS:20100630-133121655

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Abstract: The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models.

Publication: Journal of Fluid Mechanics Vol.: 642ISSN: 0022-1120

ID: CaltechAUTHORS:20100303-105410153

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Abstract: The behaviour of an initially planar shock wave propagating into a linearly convergent wedge is investigated experimentally and numerically. In the experiment, a 25° internal wedge is mounted asymmetrically in a pressure-driven shock tube. Shock waves with incident Mach numbers in the ranges of 1.4–1.6 and 2.4–2.6 are generated in nitrogen and carbon dioxide. During each run, the full pressure history is recorded at fourteen locations along the wedge faces and schlieren images are produced. Numerical simulations performed based on the compressible Euler equations are validated against the experiment. The simulations are then used as an additional tool in the investigation. The linearly convergent geometry strengthens the incoming shock repeatedly, as waves reflected from the wedge faces cross the interior of the wedge. This investigation shows that aspects of this structure persist through multiple reflections and influence the nature of the shock-wave focusing. The shock focusing resulting from the distributed reflected waves of the Mach 1.5 case is distinctly different from the stepwise focusing at the higher incoming shock Mach number. Further experiments using CO_2 instead of N_2 elucidate some relevant real-gas effects and suggest that the presence or absence of a weak leading shock on the distributed reflections is not a controlling factor for focusing.

Publication: Journal of Fluid Mechanics Vol.: 641ISSN: 0022-1120

ID: CaltechAUTHORS:20100209-094356527

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Abstract: The fluid-structure interaction simulation of detonation- and shock-wave-loaded fracturing thin-walled structures requires numerical methods that can cope with large deformations as well as topology changes. We present a robust level-set-based approach that integrates a Lagrangian thin shell finite element solver with fracture and fragmentation capabilities with an Eulerian Cartesian detonation solver with optional dynamic mesh adaptation. As an application example, the rupture of a thin aluminum tube due to the passage of an ethylene-oxygen detonation wave is presented.

Publication: Lecture Notes in Computer Science No.: 3992 ISSN: 0302-9743

ID: CaltechAUTHORS:20191009-154212803

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Abstract: An experimental and numerical study of impinging, incompressible, axisymmetric, laminar jets is described, where the jet axis of symmetry is aligned normal to the wall. Particle streak velocimetry (PSV) is used to measure axial velocities along the centerline of the flow field. The jet-nozzle pressure drop is measured simultaneously and determines the Bernoulli velocity. The flow field is simulated numerically by an axisymmetric Navier-Stokes spectral-element code, an axisymmetric potential-flow model, and an axisymmetric one-dimensional stream-function approximation. The axisymmetric viscous and potential-flow simulations include the nozzle in the solution domain, allowing nozzle-wall proximity effects to be investigated. Scaling the centerline axial velocity by the Bernoulli velocity collapses the experimental velocity profiles onto a single curve that is independent of the nozzle-to-plate separation distance. Axisymmetric direct numerical simulations yield good agreement with experiment and confirm the velocity profile scaling. Potential-flow simulations reproduce the collapse of the data; however, viscous effects result in disagreement with experiment. Axisymmetric one-dimensional stream-function simulations can predict the flow in the stagnation region if the boundary conditions are correctly specified. The scaled axial velocity profiles are well characterized by an error function with one Reynolds-number-dependent parameter. Rescaling the wall-normal distance by the boundary-layer displacement-thickness-corrected diameter yields a collapse of the data onto a single curve that is independent of the Reynolds number. These scalings allow the specification of an analytical expression for the velocity profile of an impinging laminar jet over the Reynolds number range investigated of 200<=Re<=1400.

Publication: Physical Review E Vol.: 72 No.: 6 ISSN: 1539-3755

ID: CaltechAUTHORS:BERpre05

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Abstract: This report describes an experimental and numerical study of impinging, incompressible, axisymmetric, laminar jets, where the jet axis of symmetry is aligned normal to the wall. Particle Streak Velocimetry (PSV) is used to measure axial velocities along the centerline of the flow field. The jet-nozzle pressure drop is measured simultaneously and determines the Bernoulli velocity. The flowfield is simulated numerically by an axisymmetric Navier-Stokes spectral-element code, an axisymmetric potential-flow model, and an axisymmetric one-dimensional streamfunction approximation. The axisymmetric viscous and potential-flow simulations include the nozzle in the solution domain, allowing nozzle-wall proximity effects to be investigated. Scaling the centerline axial velocity by the Bernoulli velocity collapses the experimental velocity profiles onto a single curve that is independent of the nozzle-plate separation distance. Axisymmetric direct numerical simulations yield good agreement with experiment and confirm the velocity profile scaling. Potential-flow simulations reproduce the collapse of the data, however, viscous effects result in disagreement with experiment. Axisymmetric one-dimensional streamfunction simulations can predict the flow in the stagnation region if the boundary conditions are correctly specified. The scaled axial velocity profiles are well-characterized by an error function with one Reynolds-number dependent parameter. Rescaling the wall-normal distance by the boundary-layer displacement-thickness-corrected diameter yields a collapse of the data onto a single curve that is independent of the Reynolds number. These scalings allow the specification of an analytical expression for the velocity profile of an impinging laminar jet over the Reynolds number range investigated of 200 ≤ Re ≤ 1400.

ID: CaltechGALCITFM:2005.003

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Abstract: The Center for Simulating Dynamic Response of Materials at the California Institute of Technology is constructing a virtual shock physics facility for studying the response of various target materials to very strong shocks. The Virtual Test Facility (VTF) is an end-to-end, fully three-dimensional simulation of the detonation of high explosives (HE), shock wave propagation, solid material response to pressure loading, and compressible turbulence. The VTF largely consists of a parallel fluid solver and a parallel solid mechanics package that are coupled together by the exchange of boundary data. The Eulerian fluid code and Lagrangian solid mechanics model interact via a novel approach based on level sets. The two main computational packages are integrated through the use of Pyre, a problem solving environment written in the Python scripting language. Pyre allows application developers to interchange various computational models and solver packages without recompiling code, and it provides standardized access to several data visualization engines and data input mechanisms. In this paper, we outline the main components of the VTF, discuss their integration via Pyre, and describe some recent accomplishments in large-scale simulation using the VTF.

Publication: Journal of Supercomputing Vol.: 23 No.: 1 ISSN: 0920-8542

ID: CaltechAUTHORS:20191008-073946675

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Abstract: Numerical studies of the domain chaos state in a model of rotating Rayleigh-Bénard convection suggest that finite size effects may account for the discrepancy between experimentally measured values of the correlation length and the predicted divergence near onset.

Publication: Physical Review E Vol.: 63 No.: 4 ISSN: 1063-651X

ID: CaltechAUTHORS:CROpre01

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Abstract: Numerical and analytical solutions to the steady compressible Euler equations corresponding to a compressible analogue of the linear Stuart vortex array are presented. These correspond to a homentropic continuation, to finite Mach number, of the Stuart solution describing a linear vortex array in an incompressible fluid. The appropriate partial differential equations describing the flow correspond to the compressible homentropic Euler equations in two dimensions, with a prescribed vorticity–density–streamfunction relationship. In order to construct a well-posed problem for this continuation, it was found, unexpectedly, to be necessary to introduce an eigenvalue into the vorticity–density–streamfunction equation. In the Rayleigh–Janzen expansion of solutions in even powers of the free-stream Mach number M[infty infinity], this eigenvalue is determined by a solvability condition. Accurate numerical solution by both finite-difference and spectral methods are presented for the compressible Stuart vortex, over a range of M[infty infinity], and of a parameter corresponding to a confined mass-flow rate. These also confirm the nonlinear eigenvalue character of the governing equations. All solution branches followed numerically were found to terminate when the maximum local Mach number just exceeded unity. For one such branch we present evidence for the existence of a very small range of M[infty infinity] over which smooth transonic shock-free flow can occur.

Publication: Journal of Fluid Mechanics Vol.: 409ISSN: 0022-1120

ID: CaltechAUTHORS:MEIjfm00

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Abstract: The goal of the Caltech Center is to construct a virtual test facility (VTF): a problem solving environment for full 3D parallel simulation of the dynamic response of materials undergoing compression due to shock waves. The objective is to design a software environment that will: facilitate computation in a variety of experiments in which strong shock waves impinge on targets comprising various combinations of materials; compute the target materials' subsequent dynamic response; and validate these computations against experimental data. Successfully constructing such a facility requires modeling of the highest accuracy. We must model at atomistic scales to correctly describe the material properties of the target materials and high explosives; at intermediate (meso) scales to understand the micromechanical response of the target materials; and at continuum scales to capture properly the evolution of macroscopic effects. The article outlines such a test facility. Although it is a very simplified version of the facilities found in a shock-compression laboratory, our VTF includes all the basic features, offering a problem solving environment for validating experiments and facilitating further development of simulation capabilities.

Publication: Computing in Science & Engineering Vol.: 2 No.: 2 ISSN: 1521-9615

ID: CaltechAUTHORS:20180717-150515004

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Abstract: Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data.

No.: ASCI-TR033
ID: CaltechASCI:1999.033

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Abstract: An application of the point vortex method to the singular Biot--Savart integrals used in water wave calculations is presented. The error for this approximation is shown to be a series in odd powers of h. A method for calculating the coefficients in the series is presented.

Publication: SIAM Journal on Scientific Computing Vol.: 20 No.: 2 ISSN: 1064-8275

ID: CaltechAUTHORS:HARsiamjc98

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Abstract: Introduction: This annual report describes research accomplishments for FY 98 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, tensional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dynamic response of the target materials, and validate these computations against experimental data.

ID: CaltechASCI:1998.032

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Abstract: The Richtmyer-Meshkov instability is numerically investigated for strong shocks, i.e., for hypervelocity cases. To model the interaction of the flow with non-equilibrium chemical effects typical of high-enthalpy flows, the Lighthill-Freeman ideal dissociating gas model is employed. Richtmyer's linear theory and the impulse model are extended to include equilibrium dissociation chemistry. Numerical simulations of the compressible Euler equations indicate no period of linear growth even for amplitude to wavelength ratios as small as one percent. For large Atwood numbers, dissociation causes significant changes in density and temperature, but the change in growth of the perturbations is small. A Mach number scaling for strong shocks is presented which holds for frozen chemistry at high Mach numbers. A local analysis is used to determine the initial baroclinic circulation generation for interfaces corresponding to both positive and negative Atwood ratios.

Publication: Physics of Fluids Vol.: 9 No.: 6 ISSN: 1070-6631

ID: CaltechAUTHORS:SAMpof97

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Abstract: Significant progress was made in the third year of an interdisciplinary experimental, numerical and theoretical program to extend the state of knowledge and understanding of the effects of chemical reactions in hypervelocity flows. The program addressed the key problems in aerothermochemistry that arise from.the interaction between the three strongly nonlinear effects: Compressibility; vorticity; and chemistry. Important new results included: • New data on transition in hypervelocity carbon dioxide flows • New method of free-piston shock tunnel operation for lower enthalpy • Accurate new method for computation of self-similar flows • New experimental data on flap-induced separation at high enthalpy • Insight into mechanisms active in reacting shear layers from comparison of experiment and computation • Extensive new data from Rayleigh scattering diagnostics of supersonic shear layer • Comparison of new experiments and computation of hypervelocity double-wedge flow yielded important differences • Further first-principles computations of electron collision cross-sections of CO, N_2 and NO • Good agreement between EFMO computation and experiment of flow over a cone at high incidence • Extension of LITA diagnostics to high temperature.

ID: CaltechAUTHORS:20141111-111211793

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Abstract: Numerical simulations of two-dimensional late-stage coarsening for nucleation and growth (Ostwald ripening) are performed at large-area fractions without shape restrictions. We employ efficient computational methods that allow us to study large systems. The free energy of the system we consider is composed of two different curves. Thus, the system consists of a set of isolated particles even at high-area fractions. This is totally different from the interconnected spinodal structures generated by the Cahn-Hilliard model, where the free energy is composed of a single curve. Although the domain structures are quite different, we find that the qualitative features of the structure function for both models are the same.

Publication: Physical Review E Vol.: 54 No.: 1 ISSN: 1063-651X

ID: CaltechAUTHORS:AKApre96

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Abstract: We examine the effects of compressiblity on the structure of a single row of hollowcore, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M[infty infinity] = q[infty infinity]/c[infty infinity], and the speed ratio, a = q[infty infinity]/qv, where qv is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M[infty infinity], is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.

Publication: Journal of Fluid Mechanics Vol.: 301ISSN: 0022-1120

ID: CaltechAUTHORS:ARDjfm95

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Abstract: The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Bénard convection. The size of the domains deduced from the inverse width of the Fourier spectrum is found to scale as t^1/5 for both potential and nonpotential models. The morphology of the domains and the defect structures are, however, quite different in the two cases, and evidence is presented for a second length scale in the nonpotential case growing as t^1/2.

Publication: Physical Review Letters Vol.: 75 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:CROprl95b

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Abstract: Numerical simulations of two-dimensional late-stage coarsening for nucleation and growth or Ostwald ripening are performed at area fractions 0.05 to 0.4 using the monopole and dipole approximations of a boundary integral formulation for the steady state diffusion equation. The simulations are performed using two different initial spatial distributions. One is a random spatial distribution, and the other is a random spatial distribution with depletion zones around the particles. We characterize the spatial correlations of particles by the radial distribution function, the pair correlation functions, and the structure function. Although the initial spatial correlations are different, we find time-independent scaled correlation functions in the late stage of coarsening. An important feature of the late-stage spatial correlations is that depletion zones exist around particles. A log-log plot of the structure function shows that the slope at small wave numbers is close to 4 and is -3 at very large wave numbers for all area fractions. At large wave numbers we observe oscillations in the structure function. We also confirm the cubic growth law of the average particle radius. The rate constant of the cubic growth law and the particle size distribution functions are also determined. We find qualitatively good agreement between experiments and the present simulations. In addition, the present results agree well with simulation results using the Cahn-Hilliard equation.

Publication: Physical Review E Vol.: 51 No.: 6 ISSN: 1063-651X

ID: CaltechAUTHORS:AKApre95

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Abstract: We study the chaotic domain state in rotating convection using a model equation that allows for a continuous range of roll orientations as in the experimental system. Methods are developed for extracting the domain configuration from the resulting patterns that should be applicable to a wide range of domain states. Comparison with the truncated three mode amplitude equation description is made.

Publication: Chaos Vol.: 4 No.: 4 ISSN: 1054-1500

ID: CaltechAUTHORS:CROchaos94

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Abstract: A parallel program archetype aids in the development of reliable, efficient parallel applications with common computation/communication structures by providing stepwise refinement methods and code libraries specific to the structure. The methods and libraries help in transforming a sequential program into a parallel program via a sequence of refinement steps that help maintain correctness while refining the program to obtain the appropriate level of granularity for a target machine. The specific archetype discussed here deals with the integration of task and data parallelism by using collective (or group) communication. This archetype has been used to develop several applications.

ID: CaltechCSTR:1994.cs-tr-94-08

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Abstract: A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented. The paper focuses on the following new aspects: explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem; general relationship of the convergence rate of the Uzawa procedure to classical inf-sup discretization analysis; and application of the method to high-order variational discretization.

Publication: SIAM Journal on Scientific Computing Vol.: 14 No.: 2 ISSN: 1064-8275

ID: CaltechAUTHORS:20120307-151849174

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Abstract: Theory and calculations are presented for the evolution of Richtmyer–Meshkov instability in two-dimensional continuously stratified fluid layers. The initial acceleration and subsequent instability of the fluid layer are induced by means of an impulsive pressure distribution. The subsequent dynamics of the fluid layer are then calculated numerically using the incompressible equations of motion. Initial conditions representing single-scale perturbations and multiple-scale random perturbations are considered. It is found that the growth rates for Richtmyer–Meshkov instability of stratified fluid layers are substantially lower than those predicted by Richtmyer for a sharp fluid interface with an equivalent jump in density. A frozen field approximation for the early-time dynamics of the instability is proposed, and shown to approximate the initial behavior of the layer over a time equivalent to the traversal of several layer thicknesses. It is observed that the nonlinear development of the instability results in the formation of plumes of penetrating fluid. Late in the process, the initial momentum deposited by the impulse is primarily used in the internal mixing of the layer rather than in the overall growth of the stratified layer. At intermediate times, some evidence for the existence of scaling behavior in the width of the mixing layer of the instability is observed for the multiple-scale random perturbations, but not for the single-scale perturbations. The time variation of the layer thickness differs from the scaling derived using ideas of self-similarity due to Barenblatt [Non-Linear Dynamics and Turbulence, edited by G. I. Barenblatt, G. Ioos, and D. D. Joseph (Pitman, Boston, 1983), p. 48] even at low Atwood ratio, presumably because of the inhomogeneity and anisotropy due to the excitation of vortical plumes.

Publication: Physics of Fluids A Vol.: 5 No.: 2 ISSN: 0899-8213

ID: CaltechAUTHORS:PHApofa93

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Abstract: The phenomenon of vortex reconnection is analysed numerically and the results are compared qualitatively with the predictions of a model of reconnection recently proposed by Saffman. Using spectral methods over both uniform and strained meshes, numerical simulations are performed of two nearly parallel, counter-rotating vortex tubes, over the range of Reynolds numbers Re = 1000–3500. The calculations utilizing a uniform mesh are performed for Re ≤ 1500 with a resolution of 128 points in each direction. The calculations utilizing a stretched mesh are performed for 1500 < Re ≤ 3500 with a resolution of up to 160 points in each direction and with a fourfold stretching about the region of reconnection. We present results for the variation of the maximum of vorticity, the time to reconnection, and other diagnostics of this flow as functions of the Reynolds number. From numerical simulation of the model equations, we infer and demonstrate the existence of exact solutions to the model to which its solutions arising from more general initial conditions are attracted at late times. In the limit of infinite Reynolds number, the model predicts eventual saturation of the axial strain, a feature observed in the recent work of Pumir & Siggia and also observed in our full numerical simulations. In this respect the model captures the observed local dynamics of vortex stretching. However, because the global effects of external flows are not included in the model, the model predicts that the axial strain eventually decays and the maximum vorticity grows linearly at late times. In contrast, from the full simulations, we see the possible emergence of the behaviour of the axial strain at infinite Reynolds number. As our simulations are affected by non-local effects, we do observe saturation of the strain but no subsequent decay. It is also shown analytically that the model predicts a reconnection time which varies logarithmically with increasing Reynolds number. Comparison with the full numerical simulations shows a much slower variation of the reconnection time with increasing Reynolds number than predicted by the model. Other points of agreement and disagreement between the Saffman model and the simulations are discussed, Reconnection is also discussed from the point of view of its relation to the possible onset of nearly singular behaviour of the Euler equation. In agreement with the recent numerical results of Pumir & Siggia, our results suggest that no singularity in the vorticity will form in a finite time for this initial condition.

Publication: Journal of Fluid Mechanics Vol.: 246ISSN: 0022-1120

ID: CaltechAUTHORS:20181120-153100759

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Abstract: We examine the stability to superharmonic disturbances of finite-amplitude two-dimensional travelling waves of permanent form in plane Poiseuille flow. The stability characteristics of these flows depend on whether the flux or pressure gradient are held constant. For both conditions we find several Hopf bifurcations on the upper branch of the solution surface of these two-dimensional waves. We calculate the periodic orbits which emanate from these bifurcations and find that there exist no solutions of this type at Reynolds numbers lower than the critical value for existence of two-dimensional waves ([approximate]2900). We confirm the results of Jiménez (1987) who first detected a stable branch of these solutions by integrating the two-dimensional equations of motion numerically.

Publication: Journal of Fluid Mechanics Vol.: 229ISSN: 0022-1120

ID: CaltechAUTHORS:SOIjfm91

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Abstract: The problem of calculating the kinetic energy created by impulsive acceleration of an incompressible continuously stratified fluid is formulated. Solutions are obtained for small density perturbations and a particular profile for various Atwood numbers and length scales. The kinetic energy is reduced when the undisturbed density variation is more diffuse.

Publication: Physics of Fluids A Vol.: 1 No.: 11 ISSN: 0899-8213

ID: CaltechAUTHORS:SAFpofa89b

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Abstract: The stability to three dimensional disturbances of bubbles rising rectilinearly in an inviscid fluid is studied numerically. It is found, in contrast with earlier work, that the interaction of hydrodynamic pressure forces and surface tension does not lead to linear instability of the bubble path.

Publication: Journal of Fluid Mechanics Vol.: 198ISSN: 0022-1120

ID: CaltechAUTHORS:20120510-153925560

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Abstract: With a Biot-Savart model of vortex filaments to provide initial conditions, a finite difference scheme for the incompressible Navier-Stokes equation is used in the region of closest approach of two vortex rings. In the Navier-Stokes solution, we see that the low pressure which develops between the interacting vorticity regions causes the distortion of the initially circular vortex cross section and forces the rearrangement of vorticity on a convective time scale which is much faster than that estimated from viscous transport.

Publication: Physical Review Letters Vol.: 58 No.: 16 ISSN: 0031-9007

ID: CaltechAUTHORS:ASHprl87

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Abstract: We present the first detailed calculations in the ordered phase using the massive φ4 field theory directly at d=3. It is shown that an adapted expansion allows the renormalization functions of the symmetric theory to be kept unchanged. Extending results in a previous paper [C. Bagnuls and C. Bervillier, Phys. Rev. B 32, 7209 (1985)] (noted I), we obtain, for Ising-type systems, nonasymptotic functions of temperature for the spontaneous magnetization, the susceptibility, and the specific heat along the critical isochore, which include all the quantitative universal characteristics of critical behavior in the real preasymptotic critical domain Dpreas. All universal leading- and first-correction amplitude combinations (including the new one RBcr-) are accurately estimated and are compared with previous theoretical and experimental estimates. We also show that the functions are well adapted to a suitable comparison with experiment and we describe how the adjustable parameters, limited to only three (the same as in I), enter in nonasymptotic critical behavior. Together with I, this work provides experimentalists with an efficient and coherent method which will facilitate the experimental test of the renormalization-group predictions.

Publication: Physical Review B Vol.: 35 No.: 7 ISSN: 0163-1829

ID: CaltechAUTHORS:BAGprb87

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Abstract: The representation of an inviscid three-dimensional incompressible flow by vortex singularities is considered and shown to lead to dynamical inconsistencies.

Publication: Physics of Fluids Vol.: 29 No.: 8 ISSN: 1070-6631

ID: CaltechAUTHORS:SAFpof86

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Abstract: Selection of steady needle crystals in the full nonlocal symmetric model of dendritic growth is considered. The diffusion equation and associated kinematic and thermodynamic boundary conditions are recast into a nonlinear integral equation which is solved numerically. For the range of Peclet numbers and capillarity lengths considered it is found that a smooth solution exists only if anisotropy is included in the capillarity term of the Gibbs-Thomson condition. The behavior of the selected velocity and tip radius as a function of undercooling is also examined.

Publication: Physical Review A Vol.: 33 No.: 4 ISSN: 0556-2791

ID: CaltechAUTHORS:MEIpra86

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Abstract: The stability of two-dimensional infinitesimal disturbances of the inviscid Karman vortex street of finite-area vortices is reexamined. Numerical results are obtained for the growth rate and oscillation frequencies of disturbances of arbitrary subharmonic wavenumber and the stability boundaries are calculated. The stabilization of the pairing instability by finite area demonstrated by Saffman & Schatzman (1982) is confirmed, and also Kida’s (1982) result that this is not the most unstable disturbance when the area is finite. But, contrary to Kida’s quantitative predictions, it is now found that finite area does not stabilize the street to infinitesimal two-dimensional disturbances of arbitrary wavelength and that it is always unstable except for one isolated value of the aspect ratio which depends upon the size of the vortices. This result does agree, however, with those of a modified version of Kida’s analysis.

Publication: Journal of Fluid Mechanics Vol.: 147ISSN: 0022-1120

ID: CaltechAUTHORS:20120629-113551588

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Abstract: Methods to investigate the existence of overhanging gravity waves of permanent form at the interface between two uniform fluids of different density are discussed. Numerical results which demonstrate their existence are presented.

Publication: Journal of Fluid Mechanics Vol.: 129ISSN: 0022-1120

ID: CaltechAUTHORS:20120713-073053313

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Abstract: Steady three-dimensional symmetric wave patterns for finite-amplitude gravity waves on deep water are calculated from the full unapproximated water-wave equations as well as from an approximate equation due to Zakharov. These solutions are obtained as bifurcations from plane Stokes waves. The results are in good agreement with the experimental observations of Su.

Publication: Journal of Fluid Mechanics Vol.: 124ISSN: 0022-1120

ID: CaltechAUTHORS:20120717-111917446

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Abstract: Two-dimensional numerical simulations of ablatively accelerated thin-shell fusion targets, susceptible to rupture and failure by Rayleigh–Taylor instability, are presented. The results show that nonlinear effects of Rayleigh–Taylor instability are manifested in the dynamics of the "bubble" (head of the nonlinear fluid perturbation) rather than in the dynamics of the spike (tail of the perturbation). The role of multiwavelength perturbations on the shell is clarified, and rules are presented to predict the dominant nonlinear mode-mode interactions which limit shell performance. It is also shown that the essential dynamics of strongly driven flows are governed by the classical Rayleigh–Taylor instability of an ideal, incompressible, thin fluid layer.

Publication: Physics of Fluids Vol.: 25 No.: 9 ISSN: 0031-9171

ID: CaltechAUTHORS:VERpof82

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Abstract: A vortex technique capable of calculating the Rayleigh–Taylor instability to large amplitudes in inviscid, incompressible, layered flows is introduced. The results show the formation of a steady‐state bubble at large times, whose velocity is in agreement with the theory of Birkhoff and Carter. It is shown that the spike acceleration can exceed free fall, as suggested recently by Menikoff and Zemach. Results are also presented for instability at various Atwood ratios and for fluids having several layers.

Publication: Physics of Fluids Vol.: 23 No.: 8 ISSN: 1070-6631

ID: CaltechAUTHORS:20120718-085149673

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Abstract: Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained.

Publication: Physical Review B Vol.: 17 No.: 3 ISSN: 0163-1829

ID: CaltechAUTHORS:BAKprb78

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Abstract: The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an exp(-As^4+Bs^2) spin-weight factor are expanded in the dimensionless, renormalized coupling constant. These series are summed by the Padé-Borel method to yield the critical indices γ=1.241±0.002, η=0.02±0.02, ν=0.63±0.01, and Δ1=0.49±0.01.

Publication: Physical Review Letters Vol.: 36 No.: 23 ISSN: 0031-9007

ID: CaltechAUTHORS:BAKprl76

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