Showing papers on "Shock wave published in 1994"

Dynamic Behavior of Materials

Abstract: Dynamic Deformation and Waves. Elastic Waves. Plastic Waves. Shock Waves. Shock Waves: Equations of State. Differential Form of Conservation Equations and Numerical Solutions to More Complex Problems. Shock Wave Attenuation, Interaction, and Reflection. Shock Wave-Induced Phase Transformations and Chemical Changes. Explosive-Material Interactions. Detonation. Experimental Techniques: Diagnostic Tools. Experimental Techniques: Methods to Produce Dynamic Deformation. Plastic Deformation at High Strain Rates. Plastic Deformation in Shock Waves. Shear Bands (Thermoplastic Shear Instabilities). Dynamic Fracture. Applications. Indexes.

On the hydrodynamic interaction of shock waves with interstellar clouds. 1: Nonradiative shocks in small clouds

Abstract: The interstellar medium (ISM) is inhomogeneous, with clouds of various temperatures and densities embedded in a tenuous intercloud medium. Shocks propagating through the ISM can ablate or destroy the clouds, at the same time significantly altering the properties of the intercloud medium. This paper presents a comprehensive numerical study of the simplest case of the interaction between a shock wave and a spherical cloud, in which the shock far from the cloud is steady and planar, and in which radiative losses, thermal conduction, magnetic fields, and gravitational forces are all neglected. As a result, the problem is completely specified by two numbers: the Mach number of the shock, M, and the ratio of the density of the cloud to that of the intercloud medium, Chi. For strong shocks we show that the dependence on M scales out, so the primary independent parameter is Chi. Variations from this simple case are also considered: the potential effect of radiative losses is assessed by calculations in which the ratio of specific heats in the cloud is 1.1 instead of 5/3; the effect of the initial shape of the cloud is studied by using a cylindrical cloud instead of a spherical one; and the role of the initial shock is determined by considering the case of a cloud embedded in a wind. Local adaptive mesh refinement techniques with a second-order, two-fluid, two-dimensional Godunov hydrodynamic scheme are used to address these problems, allowing heretofore unobtainable numerical resolution. Convergence studies to be described in a subsequent paper demonstrate that about 100 zones per cloud radius are needed for accurate results; previous calculations have generally used about a third of this number. The results of the calculations are analyzed in terms of global quantities which provide an overall description of te shocked cloud: the size and shape of the cloud, the mean density, the mean pressure, the mean velocity, the velocity dispersion, and the total circulation.

On the dynamics of a shock-bubble interaction

Abstract: We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanims whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas and Sturtevant.

Determining the standoff distance of the bow shock: Mach number dependence and use of models

Abstract: We explore the factors that determine the bow shock standoff distance. These factors include the parameters of the solar wind, as well as the size and shape of the obstacle. In this report we develop a semiempirical Mach number relation for the bow shock standoff distance in order to take into account the shock's behavior at low Mach numbers. This is done by determining which properties of the shock are most important in controlling the standoff distance and using this knowledge to modify the current Mach number relation. While the present relation has proven useful at higher Mach numbers, it has lacked effectiveness at the low Mach number limit. We also analyze the bow shock dependence upon the size and shape of the obstacle, noting that it is most appropriate to compare the standoff distance of the bow shock to the radius of curvature of the obstacle, as opposed to the distance from the focus of the object to the nose. Last, we focus our attention on the use of bow shock models in determining the standoff distance. We note that the physical behavior of the shock must correctly be taken into account, specifically the behavior as a function of solar wind dynamic pressure; otherwise, erroneous results can be obtained for the bow shock standoff distance.

Mass-loss rates, ionization fractions, shock velocities, and magnetic fields of stellar jets

Abstract: In this paper we calculate emission-line ratios from a series of planar radiative shock models that cover a wide range of shock velocities, preshock densities, and magnetic fields The models cover the initial conditions relevant to stellar jets, and we show how to estimate the ionization fractions and shock velocities in jets directly from observations of the strong emission lines in these flows The ionization fractions in the HH 34, HH 47, and HH 111 jets are approximately 2%, considerably smaller than previous estimates, and the shock velocities are approximately 30 km/s For each jet the ionization fractions were found from five different line ratios, and the estimates agree to within a factor of approximately 2 The scatter in the estimates of the shock velocities is also small (+/- 4 km/s) The low ionization fractions of stellar jets imply that the observed electron densities are much lower than the total densities, so the mass-loss rates in these flows are correspondingly higher (approximately greater than 2 x 10(exp -7) solar mass/yr) The mass-loss rates in jets are a significant fraction (1%-10%) of the disk accretion rates onto young stellar objects that drive the outflows The momentum and energy supplied by the visible portion of a typical stellar jet are sufficient to drive a weak molecular outflow Magnetic fields in stellar jets are difficult to measure because the line ratios from a radiative shock with a magnetic field resemble those of a lower velocity shock without a field The observed line fluxes can in principle indicate the strength of the field if the geometry of the shocks in the jet is well known

Kolmogorov‐like spectra in decaying three‐dimensional supersonic flows

Abstract: A numerical simulation of decaying supersonic turbulence using the piecewise parabolic method (PPM) algorithm on a computational mesh of 5123 zones indicates that, once the solenoidal part of the velocity field, representing vortical motions, is fully developed and has reached a self‐similar regime, a velocity spectrum compatible with that predicted by the classical theory of Kolmogorov develops It is followed by a domain with a shallower spectrum A convergence study is presented to support these assertions The formation, structure, and evolution of slip surfaces and vortex tubes are presented in terms of perspective volume renderings of fields in physical space

Detonation structures behind oblique shocks

Abstract: Detonation structures generated by wedge‐induced, oblique shocks in hydrogen–oxygen–nitrogen mixtures were investigated by time‐dependent numerical simulations. The simulations show a multidimensional detonation structure consisting of the following elements: (1) a nonreactive, oblique shock, (2) an induction zone, (3) a set of deflagration waves, and (4) a ‘‘reactive shock,’’ in which the shock front is closely coupled with the energy release. In a wide range of flow and mixture conditions, this structure is stable and very resilient to disturbances in the flow. The entire detonation structure is steady on the wedge when the flow behind the structure is completely supersonic. If a part of the flow behind the structure is subsonic, the entire structure may become detached from the wedge and move upstream continuously.

Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: Models and scaling laws

Abstract: Vorticity is deposited baroclinically by shock waves on density inhomogeneities. In two dimenslons, the circulation deposited on a planar interface may be derived analytically using shock polar analysis provided the shock refraction is regular. We present analytical expressions for Γ′, the circulation deposited per unit length of the unshocked planar interface, within and beyond the regular refraction regime. To lowest order, Γ′ scales as \[ \Gamma^\prime\propto (1-\eta^{-\frac{1}{2}})(\sin\alpha)(1+M^{-1}+2M^{-2})(M-1)(\gamma^{\frac{1}{2}}/\gamma + 1)\] where M is the Mach number of the incident shock, η is the density ratio of the gases across the interface, α is the angle between the shock and the interface and γ is the ratio of specific heats for both gases. For α ≤ 30°, the error in this approximation is less than 10% for 1.0 1, and 5.8 ≤ η ≤ 32.6 for all M. We validate our results by quantification of direct numerical simulations of the compressible Euler equations with a second-order Godunov code.We generalize the results for total circulation on non-planar (sinusoidal and circular) interfaces. For the circular bubble case, we introduce a ‘near-normality’ ansatz and obtain a model for total circulation on the bubble surface that agrees well with results of direct numerical simulations. A comparison with other models in the literature is presented.

Small amplitude theory of Richtmyer–Meshkov instability

Abstract: This paper presents a new analysis of small amplitude Richtmyer–Meshkov instability. The linear theory for the case of reflected rarefaction waves, a problem not treated in previous work, is formulated and numerically solved. This paper also carries out a systematic comparison of Richtmyer’s impulsive model to the small amplitude theory, which has identified domains of agreement as well as disagreement between the two. This comparison includes both the reflected shock and reflected rarefaction cases. Additional key results include the formulation of criteria determining the reflected wave type in terms of preshocked quantities, identification of parameter regimes corresponding to total transmission of the incident wave, discussion of an instability associated with a rarefaction wave, investigation of phase inversions and the related phenomenon of freeze‐out, and study of the sensitivity of the numerical solutions to initial conditions.

Hydrodynamic simulations of bubble collapse and picosecond sonoluminescence

Abstract: Numerical hydrodynamic simulations of the growth and collapse of a 10 μm air bubble in water were performed. Both the air and the water are treated as compressible fluids. The calculations show that the collapse is nearly isentropic until the final 10 ns, after which a strong spherically converging shock wave evolves and creates enormous temperatures and pressures in the inner 0.02 μm of the bubble. The reflection of the shock from the center of the bubble produces a diverging shock wave that quenches the high temperatures (≳30 eV) and pressures in less than 10 ps (full width at half maximum). The picosecond pulse widths are due primarily to spherical convergence/divergence and nonlinear stiffening of the air equation of state that occurs at high pressures. The results are consistent with recent measurements of sonoluminescence that had optical pulse widths less than 50 ps and 30 mW peak radiated power in the visible.

Shock interactions with magnetized interstellar clouds. 1: Steady shocks hitting nonradiative clouds

Abstract: We study the interaction of a steady, planar shock with a nonradiative, spherical, interstellar cloud threaded by a uniform magnetic field For strong shocks, the sonic Mach number scales out, so two parameters determine the evolution: the ratio of cloud to intercloud density, and the Alfven Mach number We focus on the case with initial field parallel to the shock velocity, though we also present one model with field perpendicular to the velocity Even with 100 zones per cloud radius, we find that the magnetic field structure converges only at early times However, we can draw three conclusions from our work First, our results suggest that the inclusion of a field in equipartition with the preshock medium can prevent the complete destruction of the cloud found in the field-free case recently considered by Klein, McKee, & Colella Second, the interaction of the shock with the cloud can amplify the magnetic field in some regions up to equipartition with the post-shock thermal pressure In the parallel-field case, the shock preferentially amplifies the parallel component of the field, creating a 'flux rope,' a linear structure of concentrated magnetic field The flux rope dominates the volume of amplified field, so that laminar, rather than turbulent, amplification is dominant in this case Third, the presence of the cloud enhances the production of X-ray and synchrotron emission The X-ray emission peaks early, during the initial passage of the shock over the cloud, while the synchrotron emission peaks later, when the flow sweeps magnetic field onto the axis between the cloud and the main shock

Medical applications and bioeffects of extracorporeal shock waves

Abstract: Lithotripter shock waves are pressure pulses of microsecond duration with peak pressures of 35–120 MPa followed by a tensile wave. They are an established treatment modality for kidney and gallstone disease. Further applications are pancreatic and salivary stones, as well as delayed fracture healing. The latter are either on their way to become established treatments or are currently under investigation. Shock waves generate tissue damage as a side effect which has been extensively investigated in the kidney, the liver, and the gallbladder. The primary adverse effects are local destruction of blood vessels, bleedings, and formation of blood clots in vessels. Investigations on the mechanism of shock wave action revealed that lithotripters generate cavitation both in vitro and in vivo. An increase in tissue damage at higher pulse administration rates, and also at shock wave application with concomitant gas bubble injection suggested that cavitation is a major mechanism of tissue damage. Disturbances of the heart rhythm and excitation of nerves are further biological effects of shock waves; both are probably also mediated by cavitation. On the cellular level, shock waves induce damage to cell organelles; its extent is related to their energy density. They also cause a transient increase in membrane permeability which does not lead to cell death. Administered either alone or in combination with drugs, shock waves have been shown to delay the growth of small animal tumors and even induce tumor remissions. While the role of cavitation in biological effects is widely accepted, the mechanism of stone fragmentation by shock waves is still controversial. Cavitation is detected around the stone and hyperbaric pressure suppresses fragmentation; yet major cracks are formed early before cavitation bubble collapse is observed. The latter has been regarded as evidence for a direct shock wave effect.

Structure of relativistic shocks in pulsar winds: A model of the wisps in the Crab Nebula

Abstract: We propose a model of a optical 'wisps' of the Crab Nebula, features observed in the nebular synchrotron surface brightness near the central pulsar, as manifestations of the internal structure of the shock terminating the pulsar wind. We assume that this wind is composed of ions and a much denser plasma of electrons and positrons, frozen together to a toroidal magnetic field and flowing relativistically. We construct a form of solitary wave model of the shock structure in which we self-consistently solve for the ion orbits and the dynamics of the relativistically hot, magnetized e(+/-) background flow. We ignore dispersion in the ion energies, and we treat the pairs as an adiabatic fluid. The synchrotron emission enhancements, observed as the wisps, are then explained as the regions where reflection of the ions in the self-consistent magnetic field causes compressions of the e(+/-).

Mechanisms of intraocular photodisruption with picosecond and nanosecond laser pulses

Abstract: Nd:YAG laser photodisruption with nanosecond (ns) pulses is an established method for intraocular surgery. In order to assess whether an increased precision can be achieved by the use of picosecond (ps) pulses, the plasma size, the shock wave characteristics, and the cavitation bubble expansion after optical breakdown with ps- and ns-laser pulses were investigated by time-resolved photography and acoustic measurements. Nd:YAG laser pulses with a duration of 30 ps and 6 ns, respectively, were focused into a water-filled glass cuvette. Frequency doubled light from the same laser pulses was optically delayed between 2 ns and 136 ns and used as illumination light source for photography. Since the individual events were well reproducible, the shock wave and bubble wall position could be determined as a function of time. From the slope of these r(t) curves, the shock wave and bubble wall velocities were determined, and the shock wave pressure was calculated from the shock velocity. The plasma size at various laser pulse energies was measured from photographs of the plasma radiation. The breakdown thresholds at 30 ps and 6 ns pulse duration were found to be 15 μJ and 200 μJ, respectively. At threshold, ps-plasmas are shorter than ns-plasmas, but at the same pulse energy they are always ∼2.5 times longer. The initial shock pressures were 17 kbar after ps-pulses with an energy of 50 μJ, and 21 kbar after 1 mJ ns-pulses. The pressure amplitude decayed much faster after the ps-pulses. The maximum expansion velocity of the cavitation bubble was 350 m/s after a 50 μJ ps-pulse, but 1,600 m/s after a 1 mJ ns-pulse. The side effects of intraocular microsurgery associated with shock wave emission and cavitation bubble expansion can be considerably reduced by the use of ps-pulses, and new applications of photodisruption may become possible. © 1994 Wiley-Liss, Inc.

On the mechanism of unsteady shock oscillation in shock wave/turbulent boundary layer interactions

Abstract: An experimental investigation into the mechanism of shock wave oscillation in compression ramp-generated shock wave/turbulent boundary layer interactions is presented. Particular emphasis is focused upon documenting the respective roles played by both burst-sweep events in the turbulent boundary layer immediately upstream of the interaction and the downstream separated shear layer upon unsteady shock front motion. Unlike the majority of compression ramp experiments which involve bulk separation and large-scale shock motion, consideration is given here to comparatively “weak” interactions in which the streamwise spatial excursion of the shock front is always less than one boundary layer thickness. In this manner any shock motion due to upstream burst-sweep events should be more apparent in relation to that oscillation associated with the separated region. A discrete Hilbert transform-based conditional sampling technique is used to obtain wall pressure measurements conditioned to burst-sweep events. The conditional sampling technique forms the basis by which the instantaneous shock motion is conditioned to the occurrence of upstream bursting. The relationship between the separation bubble and shock motion is also explored in detail. The results of the experiments indicate that the separation bubble represents a first-order effect on shock oscillation. Although it is demonstrated theoretically that the burst-sweep cycle can also give rise to unsteady shock motion of much lower amplitude, the experiments clearly demonstrate that there is no discernible statistical relationship between burst events and spanwise coherent shock front motion.

Postexplosion hydrodynamics of supernovae in red supergiants

Abstract: Shock propagation, mixing, and clumping are studied in the explosion of red supergiants as Type II supernovae using a two-dimensional smooth particle hydrodynamic (SPH) code. We show that extensive Rayleigh-Talor instabilities develop in the ejecta in the wake of the reverse shock wave. In all cases, the shell structure of the progenitor is obliterated to leave a clumpy, well-mixed supernova remnant. However, the occurrence of mass loss during the lifetime of the progenitor can significantly reduce the amount of mixing. These results are independent of the Type II supernova explosion mechanism.

Molecular mechanics modeling of shear and the crystal orientation dependence of the elastic precursor shock strength in pentaerythritol tetranitrate

Abstract: The elastic precursor shock strengths of pentaerythritol tetranitrate explosive crystals were measured for [100], [101], [110], and [001] orientations using velocity interferometer system for any reflector instrumentation for samples 3–6 mm thick. Input shock strength was 1.14 GPa. Measured precursor amplitudes were 0.38, 0.58, 0.98, and 1.22 GPa, respectively, for the four orientations. Critical shear stress for the slip system with the maximum resolved shear stress for each shock orientation was computed. Details of the elastic and plastic wave profiles are discussed. Molecular mechanics modeling of the shear induced by the uniaxial strain of a plane shock wave in this molecular crystal was also performed using the amber code. This may be the first application of molecular mechanics computation to a shear problem. The modeling correctly predicts the dependence of the precursor amplitude on crystal orientation for the cases considered. The results confirm the importance of steric hindrance to shear in controlling the orientation‐dependent strength in molecular crystals and sensitivity to shock initiation of detonation in molecular explosive crystals. Details of the molecular deformations and contributions to the energy barrier to inelastic shear for different orientations are given. The computational results also explain why the {110} 〈111〉 slip system is observed in quasistatic deformation in spite of having the longest Burgers vector. The dynamics of sterically hindered, shock‐induced shear is considered.

Simulation of Thick Accretion Disks with Standing Shocks by Smoothed Particle Hydrodynamics

Abstract: We present results of numerical simulation of inviscid thick accretion disks and wind flows around black holes. We use Smoothed Particle Hydrodynamics (SPH) technique for this purpose. Formation of thick disks are found to be preceded by shock waves travelling away from the centrifugal barrier. For a large range of the parameter space, the travelling shock settles at a distance close to the location obtained by a one-and-a-half dimensional model of inviscid accretion disks. Occasionally, it is observed that accretion processes are aided by the formation of oblique shock waves, particularly in the initial transient phase. The post-shock region (where infall velocity suddenly becomes very small) resembles that of the usual model of thick accretion disk discussed in the literature, though they have considerable turbulence. The flow subsequently becomes supersonic before falling into the black hole. In a large number of cases which we simulate, we find the formation of strong winds which are hot and subsonic when originated from the disk surface very close to the black hole but become supersonic within a few tens of the Schwarzschild radius of the blackhole. In the case of accretion of high angular momentum flow, very little amount of matter is accreted directly onto the black hole. Most of the matter is, however, first squeezed to a small volume close to the black hole, and subsequently expands and is expelled as a strong wind. It is quite possible that this expulsion of matter and the formation of cosmic radio jets is aided by the shock heating in the inner parts of the accretion

On the direct initiation of gaseous detonations by an energy source

Abstract: A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. These effects are first studied in a quasi-steady-state approximation valid for a characteristic timescale of evolution much larger than the reaction timescale. Analytical results for the square-wave model and numerical results for an Arrhenius law of the quasi-steady equations exhibit two branches of solutions with a C-shaped curve and a critical radius below which generalized Chapman–Jouguet (CJ) solutions cannot exist. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 300 times larger at ordinary conditions) which is the only intrinsic lengthscale in the problem. Then, the initiation of gaseous detonations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solutions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated with the critical point of the quasi-steady solutions, corresponds approximately to the boundary of the basin of attraction. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of the detonation requires a larger energy source. Transient phenomena which are associated with the intrinsic instability of the quasi-steady detonations branch develop in the induction timescale and may induce additional mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions. The criterion of initiation derived in this paper works to a good approximation and exhibits the huge numerical factor, 106–108, which has been experimentally observed in the critical value of the initiation energy.

A new class of forward‐reverse shock pairs in the solar wind

Abstract: A new class of forward-reverse shock pairs in the solar wind has been discovered using Ulysses observations at high heliographic latitudes. These shock pairs are produced by expansion of coronal mass ejections, CMEs, that have internal pressures that are higher than, and speeds that are comparable to, that of the surrounding solar wind plasma. Of six certain CMEs observed poleward of S31 deg, three have associated shock pairs of this nature. We suggest that high internal CME pressures may exist primarily for events that have high speeds close to the surface of the Sun.

Numerical investigation of separated nozzle flows

Abstract: A numerical study of axisymmetric overexpanded nozzle is presented. The flow structure of the startup and throttle-down processes are examined. During the impulsive startup process, observed flow features include the Mach disk, separation shock, Mach stem, vortex core, contact surface, slip stream, initial shock front, and shocklet. Also the movement of the Mach disk is not monotonical in the downstream direction. For a range of pressure ratios, hysteresis phenomenon occurs; different solutions were obtained depending on different processes. Three types of flow structures were observed. The location of separation point and the lower end turning point of hysteresis are closely predicted. A high peak of pressure is associated with the nozzle flow reattachment. The reversed vortical structure and affects engine performance.

Dynamics of shock waves and cavitation bubbles generated by picosecond laser pulses in corneal tissue and water

Abstract: Time-resolved flash photography was used to investigate the dynamics of shock waves and cavitation bubbles generated by picosecond optical breakdown in bovine corneal tissue and water. A picosecond Nd:YLF laser was employed. A rapid decay of the shock waves was observed in both materials, with similar temporal characteristics, indicating that water serves as a good model for shock wave studies. In contrast, differences in the cavitation bubble dynamics were found between cornea and water, which are related to differences in the mechanical and thermal properties of the two media, suggesting that water should not be used to model cavitation dynamics in cornea. The experimental results also suggest that the efficiency of intrastromal ablation may be increased by using short pulses and moderate pulse energies in order to avoid the creation of large cavitation bubbles. The experiment indicates that the optimum laser repetition rate for intrastromal ablation is between 1 and 5 kHz. © 1994 Wiley-Liss, Inc.

On the sources of interplanetary shocks at 0.72 AU

Abstract: In order to understand the solar cycle variation of interplanetary shocks and their driving source at 0.72 AU, a survey of Pioneer Venus Orbiter (PVO) magnetometer and plasma data from 1979-1988 has been conducted. Known shock drivers at 1.0 AU include coronal mass ejections (CMEs) and fast/slow stream interactions. In our analysis, CMEs were identified by a decrease in plasma temperature to background or below accompanied by an increase in plasma density and dynamic pressure. It was also required that the magnetic field exhibit a coherent rotation over about a day and an increase and decline in magnitude on a timescale of hours to days. Stream interactions were identified by a characteristic increase in ion temperature and velocity coincident with a decrease in density and a coincident increase in the total magnetic field magnitude. These signatures were usually preceded within 24 hours by a change in flow angle. In all, 45 shocks were identified: 36 driven by CMEs, 6 resulting from fast/slow stream interactions, and 3 with sources that could not be defined. The shocks driven by CMEs show a solar cycle variation that roughly follows the sunspot number. These shocks all have normals consistent with radial propagation of the shock fronts from the sun. In contrast, the few stream interaction related shocks show a tendency to occur later in the solar cycle and have a broader distribution of shock normals.

Identification of low‐frequency fluctuations in the terrestrial magnetosheath

Abstract: On the basis of magnetohydrodynamic (MHD) theory we develop a scheme for distinguishing among the four low-frequency modes which may propagate in a high-beta anisotropic plasma such as the magnetosheath: the fast and slow magnetosonic, the Alfven, and mirror modes. We use four parameters: the ratio of transverse to compressional powers in the magnetic field, the ratio of the wave powers in the thermal pressure and in the magnetic field, the ratio of the perturbations in the thermal and magnetic pressures, and the ratio of the wave powers in the velocity and in the magnetic field. In the test case of an Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) magnetosheath pass near the Sun-Earth line downstream of a quasi-perpendicular shock, the four modes can be clearly distinguished both spatially and spectrally. Near the bow shock, the waves are Alfvenic in a large frequency range, 1 to 100 mHz. In the middle and inner magnetosheath, the waves below 10 mHz are Alfvenic. The fast mode waves occur in the higher-frequency end of the enhanced spectrum, 80 mHz for the middle magnetosheath and 55 mHz for the inner sheath. The wave enhancement in the intermediate frequencies is slow modes in the inner sheath and mirror modes in the middle sheath. This confirms the earlier report of the existence of the slow mode waves near the magnetopause. These slow waves provide evidence that the magnetopause is an active source of the waves in the sheath. We also show that the measured frequency of a wave is close to an invariant if the magnetosheath flow is in a steady state. Therefore changes in the frequencies of enhanced waves indicate emergence, or damping, or mode conversion of the waves.

Focused interplanetary transport of approximately 1 MeV solar energetic protons through self-generated Alfven waves

Abstract: We present a model of the focused transport of approximately 1 MeV solar energetic protons through interplanetary Alfven waves that the protons themselves amplify or damp. It is based on the quasi-linear theory but with a phenomenological pitch angle diffusion coefficient in the 'resonance gap.' For initial Alfven wave distributions that give mean free paths greater than approximately 0.5 AU for approximately 1 MeV protons in the inner heliosphere, the model predicts greater than roughly an order of magnitude amplification (damping) in the outward (inward) propagating resonant Alfven waves at less than or approximately equal to o.3 AU heliocentric distance. As the strength of proton source is increased, the peak differential proton intensity at approximately 1 MeV at 1 AU increases to a maximum of approximately 250 particles (/(sq cm)(s)(sr)(MeV)) and then decreases slowly. It may be attenuated by a factor of 5 or more relative to the case without wave evolution, provided that the proton source is sufficiently intense that the resulting peak differential intensity of approximately 1 MeV protons at 1 AU exceeds approximately 200 particles (/(sq cm)(s)(sr)(MeV)). Therefore, in large solar proton events, (1) one may have to take into account self-amplified waves in studying solar particle propagation, (2) the number of accelerated protons escaping from a flare or interplanetary shock may have been underestimated in past studies by a significant factor, and (3) accelerated protons escaping from a traveling interplanetary shock at r less than or approximately equal to 0.3 AU should amplify the ambient hydromagnetic waves siginificantly to make the shock an efficient accelerator, even if initially the mean free path is greater than or approximately equal to 1 AU.

Shock waves in dilute bubbly liquids

Abstract: The propagation of weak shock waves in liquids containing a small concentration of gas bubbles is studied theoretically on the basis of a mathematical model that contains all - and only - the effects that contribute to first order in the gas volume fraction. In particular, the thermal exchange between the gas bubbles and the liquid is described accurately. This aspect of the theory emerges as its most significant component, relegating effects such as the relative motion between the phases to roles of minor importance. Comparison with experimental results substantiates the accuracy of the model for shock waves that have had time to broaden from an initial sharp front to a more diffuse profile. For shock waves closer to inception, marked differences are found between theory and experiment. The same problem affects all other published theoretical treatments. It is concluded that some as yet poorly understood mechanism governs the early-time behaviour of shock waves in bubbly liquids.

Nonstationary flows and shock waves

Abstract: 1. Introduction 2. Shock waves on earth and in space 3. Transition fronts 4. One-dimensional flows in a simple shock tube 5. Shock tubes with area change 6. Boundary-layer effects 7. Two-dimensional studies of oblique shock-wave reflection and diffraction 8. Spherical and cylindrical shock-tube analogues and flow simulation 10. Dusty-gas shock tube 11. Real-gas effects on shock-tube flows 12. Implosion waves and applications 13. Shock-tube construction and instrumentation 14. Closing comments Index