Showing papers on "Shock wave published in 2010"

Applied Gas Dynamics

Abstract: Preface. About the Author. 1 Basic Facts. 1.1 Definition of Gas Dynamics. 1.2 Introduction. 1.3 Compressibility. 1.4 Supersonic Flow What is it? 1.5 Speed of Sound. 1.6 Temperature Rise. 1.7 Mach Angle. 1.8 Thermodynamics of Fluid Flow. 1.9 First Law of Thermodynamics (Energy Equation). 1.10 The Second Law of Thermodynamics (Entropy Equation). 1.11 Thermal and Calorical Properties. 1.12 The Perfect Gas. 1.13 Wave Propagation. 1.14 Velocity of Sound. 1.15 Subsonic and Supersonic Flows. 1.16 Similarity Parameters. 1.17 Continuum Hypothesis. 1.18 Compressible Flow Regimes. 1.19 Summary. Exercise Problems. 2 Steady One-Dimensional Flow. 2.1 Introduction. 2.2 Fundamental Equations. 2.3 Discharge from a Reservoir. 2.4 Streamtube Area Velocity Relation. 2.5 de Laval Nozzle. 2.6 Supersonic Flow Generation. 2.7 Performance of Actual Nozzles. 2.8 Diffusers. 2.9 Dynamic Head Measurement in Compressible Flow. 2.10 Pressure Coefficient. 2.11 Summary. Exercise Problems. 3 Normal Shock Waves. 3.1 Introduction. 3.2 Equations of Motion for a Normal Shock Wave. 3.3 The Normal Shock Relations for a Perfect Gas. 3.4 Change of Stagnation or Total Pressure Across a Shock. 3.5 Hugoniot Equation. 3.6 The Propagating Shock Wave. 3.7 Reflected Shock Wave. 3.8 Centered Expansion Wave. 3.9 Shock Tube. 3.10 Summary. Exercise Problems. 4 Oblique Shock and ExpansionWaves. 4.1 Introduction. 4.2 Oblique Shock Relations. 4.3 Relation between and . 4.4 Shock Polar. 4.5 Supersonic Flow Over a Wedge. 4.6 Weak Oblique Shocks. 4.7 Supersonic Compression. 4.8 Supersonic Expansion by Turning. 4.9 The Prandtl Meyer Expansion. 4.10 Simple and Nonsimple Regions. 4.11 Reflection and Intersection of Shocks and Expansion Waves. 4.12 Detached Shocks. 4.13 Mach Reflection. 4.14 Shock-Expansion Theory. 4.15 Thin Aerofoil Theory. 4.15.1 Application of Thin Aerofoil Theory. 4.16 Summary. Exercise Problems. 5 Compressible Flow Equations. 5.1 Introduction. 5.2 Crocco's Theorem. 5.3 General Potential Equation for Three-Dimensional Flow. 5.4 Linearization of the Potential Equation. 5.5 Potential Equation for Bodies of Revolution. 5.6 Boundary Conditions. 5.7 Pressure Coefficient. 5.8 Summary. Exercise Problems. 6 Similarity Rule. 6.1 Introduction. 6.2 Two-Dimensional Flow: The Prandtl-Glauert Rule for Subsonic Flow. 6.3 Prandtl Glauert Rule for Supersonic Flow: Versions I and II. 6.4 The von Karman Rule for Transonic Flow. 6.5 Hypersonic Similarity. 6.6 Three-Dimensional Flow: Gothert s Rule. 6.7 Summary. Exercise Problems. 7 Two-Dimensional Compressible Flows. 7.1 Introduction. 7.2 General Linear Solution for Supersonic Flow. 7.3 Flow Over a Wave-Shaped Wall. 7.4 Summary. Exercise Problems. 8 Flow with Friction and Heat Transfer. 8.1 Introduction. 8.2 Flow in Constant Area Duct with Friction. 8.4 Flow with Heating or Cooling in Ducts. 8.5 Summary. Exercise Problems. 9 Method of Characteristics. 9.1 Introduction. 9.2 The Concepts of Characteristic. 9.3 The Compatibility Relation. 9.4 The Numerical Computational Method. 9.5 Theorems for Two-Dimensional Flow. 9.6 Numerical Computation with Weak Finite Waves. 9.7 Design of Supersonic Nozzle. 9.8 Summary. 10 Measurements in Compressible Flow. 10.1 Introduction. 10.2 Pressure Measurements. 10.3 Temperature Measurements. 10.4 Velocity and Direction. 10.5 Density Problems. 10.6 Compressible Flow Visualization. 10.7 Interferometer. 10.8 Schlieren System. 10.9 Shadowgraph. 10.10 Wind Tunnels. 10.11 Hypersonic Tunnels. 10.12 Instrumentation and Calibration of Wind Tunnels. 10.13 Calibration and Use of Hypersonic Tunnels. 10.14 Flow Visualization. 10.15 Summary. Exercise Problems. 11 Ramjet. 11.1 Introduction. 11.2 The Ideal Ramjet. 11.3 Aerodynamic Losses. 11.4 Aerothermodynamics of Engine Components. 11.5 Flow Through Inlets. 11.6 Performance of Actual Intakes. 11.7 Shock Boundary Layer Interaction. 11.8 Oblique Shock Wave Incident on Flat Plate. 11.9 Normal Shocks in Ducts. 11.10 External Supersonic Compression. 11.11 Two-Shock Intakes. 11.12 Multi-Shock Intakes. 11.13 Isentropic Compression. 11.14 Limits of External Compression. 11.15 External Shock Attachment. 11.16 Internal Shock Attachment. 11.17 Pressure Loss. 11.18 Supersonic Combustion. 11.19 Summary. 12 Jets. 12.1 Introduction. 12.2 Mathematical Treatment of Jet Profiles. 12.3 Theory of Turbulent Jets. 12.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis. 12.5 Expansion Levels of Jets. 12.6 Control of Jets. 12.7 Summary. Appendix. References. Index.

Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields

Abstract: Observations of a shock wave propagating through a decaying plasma in the afterglow of an impulse high-voltage nanosecond discharge and of a surface dielectric barrier discharge in the nanosecond range were analysed to determine the electron power transferred into heat in air plasmas in high electric fields. It was shown that approximately half of the discharge power can go to heat for a short (~1 µs at atmospheric pressure) period of time when reduced electric fields are present at approximately 103 Td. A kinetic model was developed to describe the processes that contribute towards the fast transfer of electron energy into thermal energy under the conditions considered. This model takes into account previously suggested mechanisms to describe observations of fast heating in moderate (~102 Td) reduced electric fields and also considers the processes that become important in the presence of high electric fields. Calculations based on the developed model agree qualitatively with analyses of high-voltage nanosecond discharge observations.

Three-dimensional Simulations of Mixing Instabilities in Supernova Explosions

Abstract: We present the first three-dimensional (3D) simulations of the large-scale mixing that takes place in the shock-heated stellar layers ejected in the explosion of a 15.5 M ? blue supergiant star. The blast is initiated and powered by neutrino-energy deposition behind the stalled shock by means of choosing sufficiently high neutrino luminosities from the contracting, nascent neutron star, whose high-density core is excised and replaced by a retreating inner grid boundary. The outgoing supernova shock is followed beyond its breakout from the stellar surface more than 2 hr after the core collapse. Violent convective overturn in the post-shock layer causes the explosion to start with significant large-scale asphericity, which acts as a trigger of the growth of Rayleigh-Taylor instabilities at the composition interfaces of the exploding star. Despite the absence of a strong Richtmyer-Meshkov instability at the H/He interface, which only a largely deformed shock could instigate, deep inward mixing of hydrogen is found as well as fast-moving, metal-rich clumps penetrating with high velocities far into the hydrogen envelope of the star as observed, for example, in the case of Supernova 1987A. Also individual clumps containing a sizeable fraction of the ejected iron-group elements (up to several 10?3 M ?) are obtained in some models. The metal core of the progenitor is partially turned over with nickel-dominated fingers overtaking oxygen-rich bullets and both nickel and oxygen moving well ahead of the material from the carbon layer. Comparing with corresponding two-dimensional (axially symmetric; 2D) calculations, we determine the growth of the Rayleigh-Taylor fingers to be faster, the deceleration of the dense metal-carrying clumps in the helium and hydrogen layers to be reduced, the asymptotic clump velocities in the hydrogen shell to be higher (up to ~4500 km s?1 for the considered progenitor and an explosion energy of 1051 erg, instead of 2000 km s?1 in 2D), and the outward radial mixing of heavy elements and inward mixing of hydrogen to be more efficient in 3D than in 2D. We present a simple argument that explains these results as a consequence of the different action of drag forces on moving objects in the two geometries.

Shock-induced heating and millisecond boiling in gels and tissue due to high intensity focused ultrasound.

Abstract: Nonlinear propagation causes high-intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency Although such nonlinear effects have been investigated previously and found to not significantly alter high-intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm(2) was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector and fluctuation of the drive voltage at the HIFU source The time to boil obtained experimentally was used to quantify heating rates and was compared with calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and measurements with a fiber optic hydrophone As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output Nonlinear heating as a result of shock waves is therefore important to HIFU, and clinicians should be aware of the potential for very rapid boiling because it alters treatments

Fast radiation mediated shocks and supernova shock breakouts

Abstract: We present a simple analytic model for the structure of non-relativistic and relativistic radiation mediated shocks. At shock velocitiessvs/c & 0.1 the shock transition region is far from thermal equilibriu m, since the transition crossing time is too short for the production of a black-body photon density (by Bremsstrahlung emission). In this region, electrons and photons (and posit rons) are in Compton (pair) equilibrium at temper- atures Ts significantly exceeding the far downstream temperature, TsTd � 2("nu¯ 3 c 3 ) 1/4 . Ts & 10 keV is reached at shock velocitiess � 0.2. At higher velocities, �s & 0.6, the plasma is dominated in the transition region by epairs and 60 keV. Ts . 200 keV. We argue that the spectrum emitted during the breaking out of supernova shocks from the stellar envelopes (or the surrounding winds) of Blue Super Giants and Wolf-Rayet stars, which reachs > 0.1 for reasonable stellar parameters, may include a hard component with photon en- ergies reaching tens or even hundreds of keV. Our breakout analysis is restricted to temperatures Ts . 50 keV corresponding to photon energies h� . 150 keV, where pair creation can be neglected. This may account for the X-ray outburst associated with SN2008D, and possibly for other SN-associated outbursts with spectra not extending beyond few 100 keV (e.g. XRF060218/SN2006aj). Subject headings: shock waves — radiation mechanisms: nonthermal — X-rays: bursts — supernovae: general : individual (SN 2008D)

EARLY UV INGRESS IN WASP-12b: MEASURING PLANETARY MAGNETIC FIELDS

Abstract: Recently, Fossati et?al. observed that the UV transit of WASP-12b showed an early ingress compared with the optical transit. We suggest that the resulting early ingress is caused by a bow shock ahead of the planetary orbital motion. In this Letter, we investigate the conditions that might lead to the formation of such a bow shock. We consider two scenarios: (1) the stellar magnetic field is strong enough to confine the hot coronal plasma out to the planetary orbit and (2) the stellar magnetic field is unable to confine the plasma, which escapes in a wind. In both cases, a shock capable of compressing plasma to the observed densities will form around the planet for plasma temperatures T (4-5) ? 106 K. In the confined case, the shock always forms directly ahead of the planet, but in the wind case the shock orientation depends on the wind speed and hence on the plasma temperature. For higher wind temperatures, the shock forms closer to the line of centers between the planet and the star. We conclude that shock formation leading to an observable early UV ingress is likely to be a common feature of transiting systems and may prove to be a useful tool in setting limits on planetary magnetic field strengths Bp . In the case of WASP-12b, we derive an upper limit of about Bp = 24 G.

Effect of Interaction Strength on Unsteadiness in Shock-Wave-Induced Separations

Abstract: The effect of the interaction strength on the unsteady behavior of a planar shock wave impinging on a low Reynolds turbulent boundary layer is investigated. This is achieved by means of a variation in incident shock angle under otherwise constant flow conditions. In addition, the effect of an order-of-magnitude variation in the Reynolds number is considered. This has been done for equivalent interaction strength, based on a similar probability of occurrence of instantaneous flow separations. The measurement technique employed is two-component planar particle image velocimetry. Common mechanisms for the large-scale reflected-shock unsteadiness are deduced by means of conditional statistics based on the separation bubble height. The results indicate that both upstream and downstream mechanisms are at work, the dominant mechanism depending on the interaction strength. No significant dependence on the Reynolds number was observed for interactions with a similar probability of instantaneous flow separations.

Excitation and emission of H2, CO and H2O molecules in interstellar shock waves

Abstract: The dissipation of kinetic energy that occurs in interstellar shock waves is accompanied by the emission of radiation. In the case of shocks that are propagating into mainly molecular gas, the emission occurs principally in lines of the species H 2 , H, O, CO and H 2 O The relative intensities of these emission lines are indicative of the type and speed of the shock wave and of the physical conditions in the ambient gas. We present the results of computations of the intensities of these lines, for small grids of models of C- and J-type shock waves, and compare with the results of previous calculations. Our results should serve to aid the interpretation of observations made with the Herschel and other satellites.

Behavior of aluminum near an ultimate theoretical strength in experiments with femtosecond laser pulses

Abstract: The dynamics of the motion of the free surface of micron and submicron films under the action of a compression pulse excited in the process of femtosecond laser heating of the surface layer of a target has been investigated by femtosecond interferometric microscopy. The relation between the velocity of the shock wave and the particle velocity behind its front indicates the shock compression to 9–13 GPa is elastic in this duration range. This is also confirmed by the small (≤1 ps) time of an increase in the parameters in the shock wave. Shear stresses reached in this process are close to their estimated ultimate values for aluminum. The spall strength determined at a strain rate of 109 s−1 and a spall thickness of 250–300 nm is larger than half the ultimate strength of aluminum.

Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation

Abstract: The interaction of a normal shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number M∞ = 1.3 and Reynolds number Reθ ≈ 1200 (based on the momentum thickness of the upstream boundary layer) is analysed by means of direct numerical simulation of the compressible Navier–Stokes equations. The computational methodology is based on a hybrid linear/weighted essentially non-oscillatory conservative finite-difference approach, whereby the switch is controlled by the local regularity of the solution, so as to minimize numerical dissipation. As found in experiments, the mean flow pattern consists of an upstream fan of compression waves associated with the thickening of the boundary layer, and the supersonic region is terminated by a nearly normal shock, with substantial bending of the interacting shock. At the selected conditions the flow does not exhibit separation in the mean. However, the interaction region is characterized by ‘intermittent transitory detachment’ with scattered spots of instantaneous flow reversal throughout the interaction zone, and by the formation of a turbulent mixing layer, with associated unsteady release of vortical structures. As found in supersonic impinging shock interactions, we observe a different amplification of the longitudinal Reynolds stress component with respect to the others. Indeed, the effect of the adverse pressure gradient is to reduce the mean shear, with subsequent suppression of the near-wall streaks, and isotropization of turbulence. The recovery of the boundary layer past the interaction zone follows a quasi-equilibrium process, characterized by a self-similar distribution of the mean flow properties.

Richtmyer-Meshkov instability: theory of linear and nonlinear evolution

Abstract: A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

Single Or Double Degenerate Progenitors? Searching For Shock Emission In The SDSS-II Type Ia Supernovae

Abstract: From the set of nearly 500 spectroscopically confirmed Type Ia supernovae (SNe) and around 10,000 unconfirmed candidates from SDSS-II, we select a subset of 108 confirmed SNe Ia with well-observed early-time light curves to search for signatures from shock interaction of the SN with a companion star. No evidence for shock emission is seen; however, the cadence and photometric noise could hide a weak shock signal. We simulate shocked light curves using SN Ia templates and a simple Gaussian shock model to emulate the noise properties of the SDSS-II sample and estimate the detectability of the shock interaction signal as a function of shock amplitude, shock width, and shock fraction. We find no direct evidence for shock interaction in the rest-frame B-band, but place an upper limit on the shock amplitude at 9% of SN peak flux (MB > - 16.6 mag). If the single degenerate channel dominates type Ia progenitors, this result constrains the companion stars to be less than about 6 M sun on the main sequence and strongly disfavors red giant companions.

Dynamics of sonic jet injection into supersonic crossflow

Abstract: The interaction between a sonic air jet and a supersonic air crossflow is simulated using large-eddy simulation (LES). A hybrid numerical methodology is used here to capture shock waves locally with minimal dissipation of the turbulent structures. The dynamic subgrid closure model employed for the LES permits a fully localized evaluation of the closure coefficients, such that there are no ad hoc adjustable parameters. Simulation of the experimental study of Santiago and Dutton (J. Propul. Power, vol. 13, 1997, pp. 264–273), where detailed measurements of the mean velocity and turbulent fluctuations have been acquired, is reported. The LES results show fairly good agreement with the experimental data for the mean and statistical fluctuations of the velocity field. The numerical study is then extended to two other jets in crossflow conditions to study the impact of the free-stream Mach number and of the jet to free-stream momentum ratio on the structure of the jet and on the dynamics of the interaction. The...

The Spiral Modes of the Standing Accretion Shock Instability

Abstract: A stalled spherical accretion shock, such as that arising in core-collapse supernovae, is unstable to non-spherical perturbations. In three dimensions, this Standing Accretion Shock Instability can develop spiral modes that spin-up the protoneutron star. Here, we study these non-axisymmetric modes by combining linear stability analysis and three-dimensional, time-dependent hydrodynamic simulations with Zeus-MP, focusing on characterizing their spatial structure and angular momentum content. We do not impose any rotation on the background accretion flow and use simplified microphysics with no neutrino heating or nuclear dissociation. Spiral modes are examined in isolation by choosing flow parameters such that only the fundamental mode is unstable for a given polar index l, leading to good agreement with linear theory. We find that any superposition of sloshing modes with non-zero relative phases survives in the nonlinear regime and leads to angular momentum redistribution. It follows that the range of perturbations required to obtain spin-up is broader than that needed to obtain the limiting case of a phase shift of {pi}/2. The bulk of the angular momentum redistribution occurs during a phase of exponential growth and arises from internal torques that are second order in the perturbation amplitude. This redistribution gives rise to at least twomore » counter-rotating regions, with the maximum angular momentum of a given sign approaching a significant fraction of the mass accretion rate times the shock radius squared ( M-dot r{sub shock}{sup 2{approx}}10{sup 47} g cm{sup 2} s{sup -1}, spin period {approx}60 ms). Nonlinear mode coupling at saturation causes the angular momentum to fluctuate in all directions with much smaller amplitudes.« less

High-precision measurements of the equation of state of hydrocarbons at 1-10 Mbar using laser-driven shock waves

Abstract: The equation of state (EOS) of polystyrene and polypropylene were measured using laser-driven shock waves with pressures from 1 to 10 Mbar. Precision data resulting from the use of α-quartz as an impedance-matching (IM) standard tightly constrains the EOS of these hydrocarbons, even with the inclusion of systematic errors inherent to IM. The temperature at these high pressures was measured, which, combined with kinematic measurements, provide a complete shock EOS. Both hydrocarbons were observed to reach similar compressions and temperatures as a function of pressure. The materials were observed to transition from transparent insulators to reflecting conductors at pressures of 1 to 2 Mbar.

Shock Breakout from Type Ia Supernova

Abstract: The mode of explosive burning in Type Ia supernovae (SNe Ia) remains an outstanding problem. It is generally thought to begin as a subsonic deflagration, but this may transition into a supersonic detonation (the delayed detonation transition, DDT). We argue that this transition leads to a breakout shock, which would provide the first unambiguous evidence that DDTs occur. Its main features are a hard X-ray flash (~20 keV) lasting ~10–2 s with a total radiated energy of ~1040 erg, followed by a cooling tail. This creates a distinct feature in the visual light curve, which is separate from the nickel decay. This cooling tail has a maximum absolute visual magnitude of MV ≈ –9 to –10 at ≈1 day, which depends most sensitively on the white dwarf radius at the time of the DDT. As the thermal diffusion wave moves in, the composition of these surface layers may be imprinted as spectral features, which would help to discern between SN Ia progenitor models. Since this feature should accompany every SNe Ia, future deep surveys (e.g., m = 24) will see it out to a distance of ≈80 Mpc, giving a maximum rate of ~60 yr-1. Archival data sets can also be used to study the early rise dictated by the shock heating (at ≈20 days before maximum B-band light). A similar and slightly brighter event may also accompany core bounce during the accretion-induced collapse to a neutron star, but with a lower occurrence rate.

Large-eddy simulation of the compressible flow past a wavy cylinder

Abstract: Numerical investigation of the compressible flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach number M ∞ =0.75 and a Reynolds number based on the mean diameter Re = 2 × 10 5 . The flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26 %, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder flow are eliminated for the wavy cylinder flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the compressible flow past a wavy surface.

On electromagnetic instabilities at ultra-relativistic shock waves

Abstract: Recent work on Fermi acceleration at ultra-relativistic shock waves has demonstrated the need for strong amplification of the background magnetic field on very short scales. Amplification of the magnetic field by several orders of magnitude has also been suggested by observations of gamma-ray bursts afterglows, both in downstream and upstream plasmas. This paper addresses this issue of magnetic field generation in a relativistic shock precursor through micro-instabilities. In a generic superluminal configuration, the level of magnetization of the upstream plasma turns out to be a crucial parameter, notably because the length scale of the shock precursor is limited by the Larmor rotation of the accelerated particles in the background magnetic field and by the speed of the shock wave. We discuss in detail and calculate the growth rates of the following beam plasma instabilities seeded by the accelerated and reflected particle populations: for an unmagnetized shock, the Weibel and filamentation instabilities, as well as the Cerenkov resonant instabilities with electrostatic modes; for a magnetized shock, the Weibel instability and the resonant Cerenkov instabilities with the longitudinal electrostatic modes, as well as the Alfven, Whisler and extraordinary modes. All these instabilities are generated upstream, then they are transmitted downstream. The modes excited by Cerenkov resonant instabilities take on particular importance with respect to the magnetization of the downstream medium since, being plasma eigenmodes, they have a longer lifetime than the Weibel modes. We discuss the main limitation of the wave growth associated with the length of precursor and the magnetization of the upstream medium for both oblique and parallel relativistic shock waves. We also characterize the proper conditions to obtain Fermi acceleration at ultra-relativistic shock waves: for superluminal shock waves, the Fermi process works for values of the magnetization parameter below some critical value, and there is an intrinsic limitation of the achievable cosmic ray energy depending on the ratio of the magnetization to its critical value. We recover results of most recent particle-in-cell simulations and conclude with some applications to astrophysical cases of interest. In particular, Fermi acceleration in pulsar winds is found to be unlikely whereas its development appears to hinge on the level of upstream magnetization in the case of ultra-relativistic gamma-ray burst external shock waves.

Three-Dimensional Simulations of MHD Turbulence Behind Relativistic Shock Waves and Their Implications for GRBs

Abstract: Relativistic astrophysical phenomena such as gamma-ray bursts (GRBs) and active galactic nuclei often require long-lived strong magnetic field. Here, we report on three-dimensional special-relativistic magnetohydrodynamic (MHD) simulations to explore the amplification and decay of macroscopic turbulence dynamo excited by the so-called Richtmyer-Meshkov instability (RMI; a Rayleigh-Taylor type instability). This instability is an inevitable outcome of interactions between shock and ambient density fluctuations. We find that the magnetic energy grows exponentially in a few eddy turnover times, and then, following the decay of kinetic turbulence, decays with a temporal power-law exponent of -0.7. The magnetic-energy fraction can reach $epsilon_B \sim$ 0.1 but depends on the initial magnetic field strength. We find that the magnetic energy grows by at least two orders of magnitude compared to the magnetic energy immediately behind the shock. This minimum degree of the amplification does not depend on the amplitude of the initial density fluctuations, while the growth timescale and the maximum magnetic energy depend on the degree of inhomogeneity in the density. The transition from Kolmogorov cascade to MHD critical balance cascade occurs at $\sim$ 1/10th the initial inhomogeneity scale, which limits the maximum synchrotron polarization to less than 2%. New results include the avoidance of electron cooling with RMI turbulence, the turbulent photosphere model via RMI, and the shallow decay of the early afterglow from RMI. We also performed a simulation of freely decaying turbulence with relativistic velocity dispersion. We find that relativistic turbulence begins to decay much faster than one eddy-turnover time because of fast shock dissipation, which does not support the relativistic turbulence model by Narayan & Kumar.

Powerful h-2 line cooling in stephan's quintet. i. mapping the significant cooling pathways in group-wide shocks

Abstract: We present results from the mid-infrared spectral mapping of Stephan's Quintet using the Spitzer Space Telescope. A 1000 km s^(-1) collision (t_(col) = 5 × 10^6 yr) has produced a group-wide shock, and for the first time the large-scale distribution of warm molecular hydrogen emission is revealed, as well as its close association with known shock structures. In the main shock region alone we find 5.0 × 10^8 M_☉ of warm H_2 spread over ~480 kpc^2 and additionally report the discovery of a second major shock-excited H_2 feature, likely a remnant of previous tidal interactions. This brings the total H2 line luminosity of the group in excess of 10^(42) erg s^(-1). In the main shock, the H_2 line luminosity exceeds, by a factor of 3, the X-ray luminosity from the hot shocked gas, confirming that the H_2-cooling pathway dominates over the X-ray. [Si II]34.82 μm emission, detected at a luminosity of 1/10th of that of the H_2, appears to trace the group-wide shock closely, and in addition, we detect weak [Fe II]25.99 μm emission from the most X-ray luminous part of the shock. Comparison with shock models reveals that this emission is consistent with regions of fast shocks (100 km s^(-1) < V_s < 300 km s^(-1)) experiencing depletion of iron and silicon onto dust grains. Star formation in the shock (as traced via ionic lines, polycyclic aromatic hydrocarbon and dust emission) appears in the intruder galaxy, but most strikingly at either end of the radio shock. The shock ridge itself shows little star formation, consistent with a model in which the tremendous H_2 power is driven by turbulent energy transfer from motions in a post-shocked layer which suppresses star formation. The significance of the molecular hydrogen lines over other measured sources of cooling in fast galaxy-scale shocks may have crucial implications for the cooling of gas in the assembly of the first galaxies.

Usage of extracorporeal and intracorporeal pressure shock waves in medicine

Abstract: A shock wave device includes multiple shock wave generators within a housing having an elongated aperture covered by a membrane. The length of the aperture exceeds the width of the aperture and the multiple generators provide shock wave fronts through the aperture and membrane for targeted application of shock waves to human and animal bodies.

First complete determination of plasma physical parameters across a coronal mass ejection-driven shock

Abstract: We report on the study of a fast coronal mass ejection (CME)-driven shock associated with the solar eruption of 2002 March 22. This event was observed in the intermediate corona both in white light and the extreme ultraviolet (EUV) by the LASCO and UVCS instruments on board the Solar and Heliospheric Observatory ,a s well as in metric and decametric wavelengths through space- and ground-based radio observatories. Clear signatures of shock transit are (1) strong type II emission lanes observed after the CME initiation, (2) strong Ovi λλ1032, 1037 line profile broadenings (up to ∼2 × 10 7 K) associated with the shock transit across the UVCS slit field of view, and (3) a density enhancement located in LASCO images above the CME front. Since the UVCS slit was centered at 4.1 R� , in correspondence with the flank of the expanding CME, this observation represents the highest UV detection of a shock obtained so far with the UVCS instrument. White-light and EUV data have been combined in order to estimate not only the shock compression ratio and the plasma temperature, but also the strength of the involved coronal magnetic fields, by applying the Rankine–Hugoniot equations for the general case of oblique shocks. Results show that, for a compression ratio X = 2.06 as derived from LASCO data, the coronal plasma is heated across the shock from an initial temperature of 2.3 × 10 5 Ku p to 1.9 × 10 6 K, while at the same time the magnetic field undergoes a compression from a pre-shock value of ∼0.02 G up to a post-shock field of ∼0.04 G. Magnetic and kinetic energy density increases at the shock are comparable (in agreement with the idea of equipartition of energy), and both are more than two times larger than the thermal energy density increase. This is the first time that a complete characterization of pre- and post-shock plasma physical parameters has been derived in the solar corona.

Analytic forms of the perpendicular cosmic ray diffusion coefficient for an arbitrary turbulence spectrum and applications on transport of Galactic protons and acceleration at interplanetary shocks

Abstract: We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.

Thermal histories of chondrules in solar nebula shocks

Abstract: Chondrules are important early Solar System materials that can provide a wealth of information on conditions in the solar nebula, if their formation mechanism can be understood. The theory most consistent with observational constraints, especially thermal histories, is the so-called shock model, in which chondrules were melted in solar nebula shocks. However, several problems have been identified with previous shock models. These problems all pertained to the treatment of the radiation field, namely, the input boundary condition to the radiation field, the proper treatment of the opacity of solids, and the proper treatment of molecular line cooling. In this paper, we present the results of our updated shock model, which corrects for the problems listed above. Our new hydrodynamic shock code includes a complete treatment of molecular line cooling due to H{sub 2}O. Previously, shock models including line cooling predicted chondrule cooling rates exceeding 10{sup 5} K hr{sup -1}. Contrary to these expectations, we have found that the effect of line cooling is minimal; after the inclusion of line cooling, the cooling rates of chondrules are 10-1000 K hr{sup -1}. The reduction in the otherwise rapid cooling rates attributable to line cooling is due to a combination of factors, includingmore » buffering due to hydrogen recombination/dissociation, high column densities of water, and backwarming. Our model demonstrates that the shock model for chondrule formation remains consistent with observational constraints.« less