Radiative shock structure.
Shock wave structure in ionized hydrogen, using Eddington approximation to solve Rankine- Hugoniot jump equation
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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.↗
The cosmic-ray shock structure problem for relativistic shocks
The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.
Webb, G. M.↗
Preliminary investigation of interplanetary shock structure: Quasi-parallel shocks
Pioneer 9's magnetic field and plasma data were studied to develop arguments for or against the observation of oblique interplanetary shocks. Structural classifications are defined, and the justification for seeking these classifications in the solar wind are presented.
Greenstadt, E. W.↗
Shock Structure Analysis and Aerodynamics in a Weakly Ionized Gas Flow
The structure of a shock wave propagating through a weakly ionized gas is analyzed using an electrofluid dynamics model composed of classical conservation laws and Gauss Law. A viscosity model is included to correctly model the spatial scale of the shock structure, and quasi-neutrality is not assumed. A detailed analysis of the structure of a shock wave propagating in a weakly ionized gas is presented, together with a discussion of the physics underlying the key features of the shock structure. A model for the flow behind a shock wave propagating through a weakly ionized gas is developed and used to analyze the effect of the ionization on the aerodynamics and performance of a two-dimensional hypersonic lifting body.
Saeks, R.↗
On the relationship between collisionless shock structure and energetic particle acceleration
Recent experimental research on bow shock structure and theoretical studies of quasi-parallel shock structure and shock acceleration of energetic particles were reviewed, to point out the relationship between structure and particle acceleration. The phenomenological distinction between quasi-parallel and quasi-perpendicular shocks that has emerged from bow shock research; present efforts to extend this work to interplanetary shocks; theories of particle acceleration by shocks; and particle acceleration to shock structures using multiple fluid models were discussed.
Kennel, C. F.↗
The Burnett shock structures in low density hypersonic flows
One-dimensional shock structures in low density hypersonic flows have been studied numerically by solving the Burnett and Navier-Stokes equations. A new lower-upper scheme has been developed to obtain the steady and stationary normal shock solutions by the time-marching technique. The new scheme directly employs the implicit finite difference method without computing the eigenvalues, and it is first-order accurate in time and second-order accurate in space. The computed shock structures have been compared with available experimental data, and they are in good agreements. Numerical results show that the Burnett calculations has less numerical diffusion than the Navier-Stokes calculations does. As to the shock thickness, the Burnett solutions are apparently superior than the Navier-Stokes solutions.
Liaw, Goang-Shin↗
Comparison of Burnett, super-Burnett and Monte Carlo solutions for hypersonic shock structure
The continuum Navier-Stokes, Burnett, and super-Burnett equations are solved for one-dimensional shock structures in various monoatomic gases. Solutions for a hard sphere gas, argon, and a Maxwellian gas from Mach 1.3 to Mach 50 are obtained. A numerical method utilizing the complete time-dependent continuum equations and obtaining the steady-state shock structure by allowing the system to relax from arbitrary initial conditions is employed. Shock density, velocity, temperature, and entropy profiles are also obtained using the direct simulation Monte Carlo method, and these results are used as bases for comparison for continuum solution profiles. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Solutions to the super-Burnett equations with coefficients as presently derived, however, are considered to be inferior to those of the Burnett equations.
Fiscko, Kurt A.↗
Comparison of shock structure solutions using independent continuum and kinetic theory approaches
A vehicle traversing the atmosphere will experience flight regimes at high altitudes in which the thickness of a hypersonic shock wave is not small compared to the shock standoff distance from the hard body. When this occurs, it is essential to compute accurate flow field solutions within the shock structure. In this paper, one-dimensional shock structure is investigated for various monatomic gases from Mach 1.4 to Mach 35. Kinetic theory solutions are computed using the Direct Simulation Monte Carlo method. Steady-state solutions of the Navier-Stokes equations and of a slightly truncated form of the Burnett equations are determined by relaxation to a steady state of the time-dependent continuum equations. Monte Carlo results are in excellent agreement with published experimental data and are used as bases of comparison for continuum solutions. For a Maxwellian gas, the truncated Burnett equations are shown to produce far more accurate solutions of shock structure than the Navier-Stokes equations.
Fiscko, Kurt A.↗
Hypersonic shock structure with Burnett terms in the viscous stress and heat flux
The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.
Chapman, Dean R.↗
Shock structure in transversely impinging jet flows.
Shock structure in two dimensional or axisymmetric jet flows under transverse impingement by low energy jets
Abdelhamid, A. N.↗
Dual satellite observations of earth's bow shock. III - Field determined shock structure
Earth bow shock configuration model from dual satellite observation
Binsack, J. H.↗
Collisionless shock structures of Earth and other planets
This report summarizes the closing segment of our multi-spacecraft, multi-instrument study of collisionless shock structure. In this last year of our study, we have necessarily concentrated on subjects that limited time and remaining resources could be expected to bring to reasonable stopping points, if not full conclusions. Our attention has been focused therefore on matters that were either well underway when the year began or that could be expected to yield rapidly completed reports publishable quickly in abbreviated versions. Contemporary publication delays prevent any new initiatives from reaching the literature within the year in the best of circumstances. The topics that fell into these categories were detailed plasma wave (pw) phenomenology in slow shocks in the Earth's distant geomagnetic tail, instantaneous orientations of theta(sub Bn) in quasiparallel (Q(sub parallel)) shock structure, and a comprehensive overview of the relationship between structural ULF waves in the Qll shock environment and waves in the magnetosphere, i.e. geomagnetic ULF pulsations. The remainder of this report describes our freshly completed results, discusses two related investigations of pw waves in the foreshock and magnetosheath, and appends the abstracts of published papers and the texts of papers in press.
Greenstadt, Eugene W.↗
Shock Structure and Magnetic Fields Generation Associated with Relativistic Jets Unmagnetized Pair Plasma
Using 3D and 2D particle-in-cell simulations we investigate a shock structure, magnetic field generation, and particle acceleration associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized pair plasma. The simulations use long computational grids which allow to study the formation and dynamics of the system in a spatial and temporal way. We find for the first time a relativistic shock system comparable to a predicted magnetohydrodynamic shock structure consisting of leading and trailing shocks separated by a contact discontinuity. Strong electromagnetic fields resulting from the Weibel two-stream instability are generated in the trailing shock where jet matter is thermalized and decelerated. We analyze the formation and nonlinear development through saturation and dissipation of those fields and associated particle acceleration. In the AGN context the trailing shock corresponds to the jet shock at the head of a relativistic astrophysical jet. In the GRB context this trailing shock can be identified with the bow shock driven by relativistic ejecta. The strong electromagnetic field region in the trailing shock provides the emission site for the hot spot at the leading edge of AGN jets and for afterglow emission from GRBs.
Niemiec, J.↗
Time-dependent evolution of cosmic-ray-modified shock structure: Transition to steady state
Steady state solutions to the two-fluid equations of cosmic-ray-modified shock structure were investigated first by Drury and Volk (1981). Their analysis revealed, among other properties, that there exist regions of upstream parameter space where the equations possess three different downstream solutions for a given upstream state. In this paper we investigate whether or not all these solutions can occur as time-asymptotic states in a physically realistic evolution. To do this, we investigate the time-dependent evolution of the two-fluid cosmic-ray equations in going from a specified initial condition to a steady state. Our results indicate that the time-asymptotic solution is strictly single-valued, and it undergoes a transition from weakly to strongly cosmic-ray-modified at a critical value of the upstream cosmic ray energy density. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence the time-dependent evolution of the shock, but it is not found to be a stable time-asymptotic state. Timescales for convergence to these states and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced model for the injection of seed particles into the shock accelerated cosmic-ray population. The injection is found to result in a more strongly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, the downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test particles.
Donohue, D. J.↗
Shock structure in jets of arbitrary exit geometry
The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.
Morris, P. J.↗
Analysis and design of numerical schemes for gas dynamics. 2: Artificial diffusion and discrete shock structure
The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristics splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP scheme in which the coefficients of the pressure differences is fully determined by the coefficient of convective diffusion. It is also shown how both the characteristic and CUSP schemes can be modified to preserve constant stagnation enthalpy in steady flow, leading to four variants, the E and H-characteristic schemes, and the E and H-CUSP schemes. Numerical results are presented which confirm the properties of these schemes.
Jameson, Antony↗
The bow shock structure of IRS 7 - Wind-wind collision near the Galactic center
New structural details of ionized gas associated with IRS 7, a mass-losing supergiant near the Galactic center, are reported, and radio continuum and theoretical maps are compared. High-resolution multiconfiguration VLA observations of IRS 7 reveal ionized gas with a bow shock structure at a wavelength of 2 cm. The apex of the bow shock is facing more toward the cluster of blue stellar objects, known as IRS 16, than Sgr A*, the compact nonthermal source near the Galaxy's dynamical center. It is inferred that the shape of the mass-losing envelope of IRS 7 is influenced by Galactic winds from IRS 16. It is concluded from a comparison of the morphology of the ionized envelope of IRS 7 with simple theoretical modeling of the bow shock structure that the shape of the shock results from the collision between the Galactic center and stellar winds rather than from the motion of IRS 7 through the interstellar medium.
Yusef-Zadeh, Farhad↗