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DOE OSTI2012

Effect of compressibility on strong shock and turbulence interactions

The interactions between turbulent flows and shock waves are important in many natural processes as well as scientific and engineering applications. One of the fundamental building blocks in these complex processes and applications is the canonical problem of isotropic turbulence and a normal shock. Unfortunately, even this fundamental problem is not well understood. Recent direct numerical simulation (DNS) results of perfect gas flow showed some new trends in turbulent statistics as mean Mach number is increased. In this paper, we first conduct extensive DNS studies on canonical strong shock and turbulence interaction problem of perfect gas flow with mean Mach numbers ranging from 2 to 30, with the emphasis on investigating the effect of compressibility. The results show that maximum values of variance of streamwise vorticity fluctuations first increase and then decrease as shock strength is increased. The peak of streamwise vorticity fluctuations is observed for shock and turbulence interactions with Mach 2.8 shock. For stronger than Mach 2.8 shocks, there is a decrease in streamwise vorticity fluctuations. The amplification of Reynolds stress R11 decreases as mean Mach number is increased till 8.8, which is consistent with findings of linear interaction analysis. This trend, however, reverses as shock strength is increased beyond Mach 8.8. For stronger than Mach 8.8 shocks, Reynolds stress R11 is amplified as mean Mach number keeps increasing. Since gas temperature increases dramatically after strong shocks, we are also working on DNS of nonequilibrium flow, where non-equilibrium flow effects including internal energy excitations, translation-vibration energy relaxation, and chemical reactions among different species are considered based on the 5-species air chemistry and recently thermal property models. The code and corresponding thermo-chemical models have been tested on two cases of non-equilibrium flow over cylinders.

Wang, Xiaowen↗

DOE OSTI2016

A reverse shock in GRB L60509A

We present the second multi-frequency radio detection of a reverse shock in a γ-ray burst. By combining our extensive radio observations of the Fermi-Large Area Telescope γ-ray burst 160509A at z = 1.17 up to 20 days after the burst with Swift X-ray observations and ground-based optical and near-infrared data, we show that the afterglow emission comprises distinct reverse shock and forward shock contributions: the reverse shock emission dominates in the radio band at ≲10 days, while the forward shock emission dominates in the X-ray, optical, and near-infrared bands. Through multi-wavelength modeling, we determine a circumburst density of n{sub 0}≈10{sup −3} cm{sup −3}, supporting our previous suggestion that a low-density circumburst environment is conducive to the production of long-lasting reverse shock radiation in the radio band. We infer the presence of a large excess X-ray absorption column, N {sub H} ≈ 1.5 × 10{sup 22} cm{sup −2}, and a high rest-frame optical extinction, A {sub V} ≈ 3.4 mag. We identify a jet break in the X-ray light curve at t{sub jet}≈6 days, and thus derive a jet opening angle of θ{sub jet}≈4{sup ∘}, yielding a beaming-corrected kinetic energy and radiated γ-ray energy of E{sub K}≈4×10{sup 50} erg and E{sub γ}≈1.3×10{sup 51} erg (1–10{sup 4} keV, rest frame), respectively. Consistency arguments connecting the forward shocks and reverse shocks suggest a deceleration time of t{sub dec} ≈460 s ≈ T {sub 90}, a Lorentz factor of Γ(t{sub dec})≈330, and a reverse-shock-to-forward-shock fractional magnetic energy density ratio of R{sub B}≡ϵ{sub B,RS}/ϵ{sub B,FS}≈8. Our study highlights the power of rapid-response radio observations in the study of the properties and dynamics of γ-ray burst ejecta.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Electron Pre-acceleration at Nonrelativistic High-Mach-number Perpendicular Shocks

We perform particle-in-cell simulations of perpendicular nonrelativistic collisionless shocks to study electron heating and pre-acceleration for parameters that permit the extrapolation to the conditions at young supernova remnants. Our high-resolution large-scale numerical experiments sample a representative portion of the shock surface and demonstrate that the efficiency of electron injection is strongly modulated with the phase of the shock reformation. For plasmas with low and moderate temperature (plasma beta β{sub p}=5⋅10{sup −4} and β{sub p}=0.5), we explore the nonlinear shock structure and electron pre-acceleration for various orientations of the large-scale magnetic field with respect to the simulation plane, while keeping it at 90° to the shock normal. Ion reflection off of the shock leads to the formation of magnetic filaments in the shock ramp, resulting from Weibel-type instabilities, and electrostatic Buneman modes in the shock foot. In all of the cases under study, the latter provides first-stage electron energization through the shock-surfing acceleration mechanism. The subsequent energization strongly depends on the field orientation and proceeds through adiabatic or second-order Fermi acceleration processes for configurations with the out-of-plane and in-plane field components, respectively. For strictly out-of-plane field, the fraction of suprathermal electrons is much higher than for other configurations, because only in this case are the Buneman modes fully captured by the 2D simulation grid. Shocks in plasma with moderate β{sub p} provide more efficient pre-acceleration. The relevance of our results to the physics of fully 3D systems is discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

Turbulence in electrostatic ion acoustic shocks

Three types of collisionless electrostatic ion acoustic shocks are investigated using a double plasma (DP) device: (1) laminar shocks; (2) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (3) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distrubution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Means, R. W.↗

NASA NTRS1973

Turbulence in electrostatic ion-acoustic shocks

Three types of collisionless electrostatic ion-acoustic shocks are investigated using the University of California, Los Angeles, double plasma device: (1) laminar shocks; (2) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (3) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distribution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Means, R. W.↗

NASA NTRS1976

A summary of observations of the earth's bow shock

The earth's bow shock can be regarded as a fast steady-state collisionless magnetohydrodynamic shock exhibiting a wide range of plasma parameter values or as an example of superalfvenic flow of a MHD fluid past a blunt body. This paper summarizes our knowledge of the bow shock. Satellite crossings of the shock have given some empirical data on the position and shape of the bow shock. Theoretical calculations on position and shape show the critical nature of the Alfven number. The main physical process to be explained with regard to the bow shock is the mechanism of thermalization of the upstream solar wind. Some of the main classes of shocks observed are quasi-parallel shocks, low Mach number laminar shocks, and high beta shocks.

Fairfield, D. H.↗

NASA NTRS1979

Shock metamorphism of granulated lunar basalt

The paper deals with an extensive series of shock-recovery experiments performed on both nonporous crystalline basalt and its granulated and sieved counterpart to study the role of porosity and grain size in shock motomorphic effects under otherwise identical conditions. Shocked samples are compared with unshocked starting material in terms of textural and mineralogical modifications attributable to shock. A comparative petrographic and chemical characterization is presented of pulverized and sieved lunar basalt 75035 shocked between 6 and 75 GPa in comparison with holocrystalline disks of the same basalts shocked in 10 earlier experiments. Specifically, a petrographic classification of shock features is given, along with an estimation of relative amounts of shock glasses and a chemical characterization of shock glasses in each shocked granular basalt.

Schaal, R. B.↗

NASA NTRS1980

Location and propagation of shock associated noise from supersonic jets

Shock associated noise from unheated supersonic jets is investigated through acoustic measurements in both the near and far fields. The peak Helmholtz number of broadband shock noise is found to be independent of nozzle pressure ratio when based on the length of the shock cells and the ambient speed of sound. This indicates that the acoustic wavelengths generated in the shock noise process are limited in size by the shock cell spacing. Excellent agreement between power spectral densities measured at various far-field angles is obtained at and above the peak shock noise frequency when source convection effects are included. Results show a directivity of broadband shock noise pointed in the upstream direction, with omnidirectionality being approached only at high pressure ratios. The relative importance of shock noise with respect to jet mixing noise is found to be maximum near the pressure ratio at which a Mach disc begins to form in the jet. Near-field measurements point to the downstream shock cells as the region where the dominant shock noise eminates from the jet.

Norum, T. D.↗

NASA NTRS1980

Aerodynamic aspects of shock containing jet plumes

Aerodynamic and acoustic measurements of shock-free and shock-containing plumes were acquired for several supersonic free-jet model nozzles. The purpose was to investigate important features of the broadband shock noise generation process. The aerodynamic measurements include the variation of shock cell spacing and strength as a function of nozzle pressure ratio, and longitudinal turbulent-mass-flux axial development as determined by a hot-film probe. In addition, correlations of the hot-film probe with a near-field microphone were obtained. These measurements provide useful information concerning the relation of peak shock noise frequency and level with variations in shock cell spacing and strength. In general, it is shown that a distinction must be made between plumes containing weak and strong imbedded shocks. Strong shocks diminish the level of emitted shock noise and influence the behavior of the jet mixing noise process. The probable location and spectral content for the shock-shear layer interaction mechanism is indicated by the correlations. Numerical inviscid plume comparisons with experimental data are also included.

Seiner, J. M.↗

NASA NTRS1982

CAS22 - FORTRAN program for fast design and analysis of shock-free airfoil cascades using fictitious-gas concept

A user-oriented computer program, CAS22, was developed that is applicable to aerodynamic analysis and transonic shock-free redesign of existing two-dimensional cascades of airfoils. This FORTRAN program can be used: (1) as an analysis code for full-potential, transonic, shocked or shock-free cascade flows; (2) as a design code for shock-free cascades that uses Sobieczky's fictitious-gas concept; and (3) as a shock-free design code followed automatically by the analysis in order to confirm that the newly obtained cascade shape provides for an entirely shock-free transonic flow field. A four-level boundary-conforming grid of an O type is generated. The shock-free design is performed by implementing Sobieczky's fictitious-gas concept of elliptic continuation from subsonic into supersonic flow domains. Recomputation inside each supersonic zone is performed by the method of characteristics in the rheograph plane by using isentropic gas relations. Besides converting existing cascade shapes with multiple shocked supersonic regions into shock-free cascades, CAS22 can also unchoke previously choked cascades and make them shock free.

Dulikravich, D. S.↗

NASA NTRS1983

The association of energetic particles and shocks in the heliosphere

The observational and theoretical work on heliospheric shocks and cosmic rays in the recent past is surveyed. The data have come mainly from spacecraft in the regions from 0.3-25 AU, and include detection of particles and plasma waves upstream of the earth's bow shock. The theory of shock acceleration is reviewed, together with analytical models of energetic particle enhancement in association with shocks or shocks within the heliosphere. It has been determined that shocks in the heliosphere are associated with energetic suprathermal particles, which are conversely all associated with shocks. Solar cosmic rays and other anomalous components are therefore accelerated by shocks, a factor that is significant for studies of the acceleration mechanisms for galactic cosmic rays. The Solar Polar Mission will provide data on all solar latitudes, and the ISEE-3 spacecraft will continue to gather information on shock accelerated ions in travelling interplanetary shock waves.

Lee, M. A.↗

NASA NTRS1984

Infrared spectroscopy of interstellar shocks

Infrared emission lines from interstellar shocks provide valuable diagnostics for violent events in the interstellar medium, such as supernova remnants and mass outflow from young stellar objects. There are two types of interstellar shocks: in J shocks, gas properties 'jump' from their preshock to their postshock values in a shock front with a thickness equal to or less than one mean free path; radiation is emitted behind the shock front, primarily in the visible and ultraviolet, but with a few strong infrared lines, such as OI(63 microns). Such shocks occur in ionized or neutral atomic gas, or at high velocities (equal to or greater than 50 km/s) in molecular gas. In C shocks, gas is accelerated and heated by collisions between charged particles, which have a low concentration and are coupled to the magnetic field, and neutral particles; radiation is generated throughout the shock and is emitted almost entirely in infrared emission lines. Such shocks occur in weakly ionized molecular gas for shock velocities below about 50 km/s.

Mckee, C. F.↗

NASA NTRS1985

Selfsimilar time dependent shock structures

Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.

Beck, R.↗

NASA NTRS1986

Observations of shock acceleration processes in the solar wind

Substantial evidence was accumulated over more than two decades that ion acceleration occurs at all collisionless shocks sampled directly in the solar system. The various shock waves in the heliosphere and the associated energetic particle phenomena are shown schematically. Three shocks have attracted considerable attention in recent years: corotating shocks due to the interaction of fast and slow solar wind streams during solar minimum, travelling interplanetary shocks due to coronal mass ejections, and planetary bow shocks. The signatures of these shocks and of their energetic particles are briefly reviewed. The most prominent theoretical models for shock acceleration are also reviewed. Recent observations at the earth's bow shock and at quasi-parallel interplanetary shocks are discussed in detail.

Scholer, M.↗

NASA NTRS1986

The chemical shock tube as a tool for studying high-temperature chemical kinetics

Although the combustion of hydrocarbons is our primary source of energy today, the chemical reactions, or pathway, by which even the simplest hydro-carbon reacts with atmospheric oxygen to form CO2 and water may not always be known. Furthermore, even when the reaction pathway is known, the reaction rates are always under discussion. The shock tube has been an important and unique tool for building a data base of reaction rates important in the combustion of hydrocarbon fuels. The ability of a shock wave to bring the gas sample to reaction conditions rapidly and homogeneously makes shock-tube studies of reaction kinetics extremely attractive. In addition to the control and uniformity of reaction conditions achieved with shock-wave methods, shock compression can produce gas temperatures far in excess of those in conventional reactors. Argon can be heated to well over 10 000 K, and temperatures around 5000 K are easily obtained with conventional shock-tube techniques. Experiments have proven the validity of shock-wave theory; thus, reaction temperatures and pressures can be calculated from a measurement of the incident shock velocity. A description is given of the chemical shock tube and auxiliary equipment and of two examples of kinetic experiments conducted in a shock tube.

Brabbs, Theodore A.↗

NASA NTRS1985

Collisionless shocks in the heliosphere: Reviews of current research

The present conference on heliospheric collisionless shocks considers such macrostructure-, microstructure-, and particle acceleration-related topics as interplanetary shock phenomena near and within 1 AU, as well as beyond, planetary bow shocks, shock formation and evolution in the solar atmosphere, MHD and gasdynamic theories for planetary bow waves, and subcritical collisionless shock waves. Also discussed are ion reflection, gyration, and dissipation at supercritical shocks, the numerical simulation of quasi-perpendicular collisionless shocks, electron distributions near collisionless shocks, the microtheory of collisionless shock current layers, plasma waves and instabilities, the electron foreshock, upstream suprathermal ions, and both diffusive and shock drift acceleration.

Tsurutani, Bruce T.↗

NASA NTRS1990

The merging of quasiperpendicular collisionless shocks

The overtaking of one collisionless shock by another is studied by means of hybrid numerical simulations. The two shocks merge into a stronger shock and trailing nonshock discontinuities. The strong shock continues to propagate in the same direction as the two weaker shocks. The merging is shown to occur by a self-consistent process involving the interaction of ions reflected at the overtaking shock with the plasma upstream of the leading shock. The characteristic time scale for the merging is typically 1/Omega(i), where Omega(i) is the ion gyrofrequency. For exactly perpendicular shocks, the trailing discontinuity is a tangential discontinuity. It has a width of 2-3 ion Larmor radii. For oblique shocks, a contact discontinuity is present in the downstream plasma state. These results are of relevance to shock interactions in the very distant solar wind as well as in other energetic astrophysical situations such as solar flares.

Cargill, P. J.↗

NASA NTRS1991

Electrostatic potential jump across fast-mode collisionless shocks

The electrostatic potential jump across fast-mode collisionless shocks is examined by comparing published observations, hybrid simulations, and a simple model, in order to better characterize its dependence on the various shock parameters. In all three, it is assumed that the electrons can be described by an isotropic power-law equation of state. The observations show that the cross-shock potential jump correlates well with the shock strength but shows very little correlation with other shock parameters. Assuming that the electrons obey an isotropic power law equation of state, the correlation of the potential jump with the shock strength follows naturally from the increased shock compression and an apparent dependence of the power law exponent on the Mach number which the observations indicate. It is found that including a Mach number dependence for the power law exponent in the electron equation of state in the simple model produces a potential jump which better fits the observations. On the basis of the simulation results and theoretical estimates of the cross-shock potential, it is discussed how the cross-shock potential might be expected to depend on the other shock parameters.

Mandt, M. E.↗