On the stability and structure of shock waves in interplanetary space
Structure of interplanetary shock waves formed by interaction of geomagnetic field and solar wind - earth bow shock
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Structure of interplanetary shock waves formed by interaction of geomagnetic field and solar wind - earth bow shock
A new electromagnetic quasi-neutral time-dependent implicit hybrid model for simulating the slow-mode switch-off shock is developed, in which the electrons are treated as a finite-mass adiabatic fluid (gamma sub e = 5/3), whose motion along the shock normal provides local charge neutrality. The model is used to examine the effects of various boundary conditions applied during shock formation. It is shown that, for each upstream condition, two distinctly different slow-shock structures can be obtained: a low-shock structure with a trailing magnetic wave (TMW) and a slow-shock structure without a TMW, depending strongly on the boundary conditions for the electric and magnetic fields at the physical piston which generates the shock. The results indicate that the slow-shock structure with a TMW is nonlinearly unstable with respect to changes in the upstream magnetic field, suggesting that the downstream structure of slow shocks need not be associated with a TMW.
Newtonian hypersonic theory for normal shock wave structure, discussing asymptotic solutions and three layer models
Structure of plane magnetohydrodynamic shock wave in rarefied fully ionized plasma
The detailed properties of sonic booms have to be better understood before commercial, next generation, supersonic and hypersonic aircraft can be properly developed. Experimental tests and measurements are needed to help sort the physical details of the flows at realistic test conditions. Some of these tests can be made in wind tunnels, but the need for full flight conditions simulation, the problem of tunnel wall interference, and the short distance the shocks can be examined from the aircraft, limit the usefulness of wind tunnel tests. Previous measurement techniques for examining the flow field of aircraft in flight have included pressure measurements on the aircraft, ground based pressure measurements, and flow field measurements made with chase aircraft. Obtaining data with chase planes is a slow and difficult process, and is limited in how close it can be obtained to the test aircraft. A need clearly existed for a better technique to examine the shock structure from the plane to large distances from the plane. A new technique has been recently developed to obtain schlieren photographs of aircraft in flight (SAF). Preliminary results have been obtained, and the technique holds promise as a tool to study the shape and approximate strength of the shock wave structure around the test aircraft, and examine shock wave details all the way from the aircraft to near the ground. The current paper describes this approach, and gives some preliminary test results.
Shock wave structure in recombining low density plasma flow, noting electron density and temperature distributions
Shock wave structure prediction by nonlinear kinetic models with Monte Carlo solutions of full Boltzmann equation
ISEE 1 and 2 spacecraft magnetic field data are used to determine the scale lengths of various elements of shock structure, as well as wavelengths and wave polarizations, in a study of structural elements which include shock ramps and precursor wave trains over a series of oblique, low Mach number terrestrial bow shocks. Dissipative processes are reflected in the damping of the precursors, and dissipative scale lengths are of 200-800 km, or several times greater than shock thicknesses. The source of dissipation in the shocks does not appear to be the wave-wave decay of the whistlers, for which no evidence is found. The interaction of the whistler itself with upstream electrons is suggested as a simple and self-consistent explanation for the observed wave train damping.
Shock metamorphosed rocks and shock-produced melt glasses from the Wanapitei Lake impact structure have been examined petrographically and by electron microprobe. Eleven clasts exhibiting varying degrees of shock metamorphism and eight impact-produced glasses have been analyzed for Rb, Sr and Sr isotopic composition. Five clasts and one glass have also been analyzed for large ion lithophile (LIL) trace element abundances including Li, Rb, Sr, and Ba and the REE's. The impact event forming the Wanapitei Lake structure occurred 37 m.y. ago based on K/Ar dating of glass and glassy whole-rock samples. Rb/Sr isotopic dating failed to provide a meaningful whole-rock or internal isochron. The isotopic composition of the glasses can be explained by impact-produced mixing and melting of metasediments.
Multiple pulsed Rayleigh imaging and filtered Rayleigh scattering are used to generate images of a complex boundary layer structure, shock wave/boundary layer interactions, and crossing shock waves. Time-sequenced Rayleigh images taken with a visible, double-pulsed laser system show the evolution of boundary layer structure of the internal flow in a generic cross-shock inlet. The images taken in the inlet give insight into 3D effects caused by the inlet geometry and may be used for modeling the complex flows.
The detailed flow structure of a normal shock wave for a gas mixture is investigated using the direct-simulation Monte Carlo method. A variable diameter hard-sphere (VDHS) model is employed to investigate the effect of different viscosity temperature exponents (VTE) for each species in a gas mixture. Special attention is paid to the irregular behavior in the density profiles which was previously observed in a helium-xenon experiment. It is shown that the VTE can have substantial effects in the prediction of the structure of shock waves. The variable hard-sphere model of Bird shows good agreement, but with some limitations, with the experimental data if a common VTE is chosen properly for each case. The VDHS model shows better agreement with the experimental data without adjusting the VTE. The irregular behavior of the light-gas component in shock waves of disparate mass mixtures is observed not only in the density profile, but also in the parallel temperature profile. The strength of the shock wave, the type of molecular interactions, and the mole fraction of heavy species have substantial effects on the existence and structure of the irregularities.
Shock wave structure of gas having rotational and vibrational relaxation, calculated with one dimensional Navier-Stokes and relaxation equations
A linear solution modeling the shock cell structure of an axisymmetric supersonic jet operated at off-design conditions is developed by the method of multiple-scales. The model solution takes into account the gradual spatial change of the mean flow in the downstream direction. Turbulence in the mixing layer of the jet has the tendency of smoothing out the sharp velocity and density gradients induced by the shocks. To simulate this effect, eddy viscosity terms are incorporated in the model. It is known that the interaction between the quasi-periodic shock cells and the downstream propagating large turbulence structures in the mixing layer of the jet is responsible for the generation of broadband shock associated noise. Experimentally, the dominant part of this noise has been found to originate from the part of the jet near the end of the potential core. Calculated shock cell spacing at the end of the jet core according to the present model is used to estimate the peak frequencies of the shock associated noise for a range of observation angles. Very favorable agreement with experimental measurements is found.
Plasma instabilities excited in collisionless shocks are responsible for particle acceleration, generation of magnetic fields , and associated radiation. We have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic-like shock structure. The shock structure depends on the composition of the jet and ambient plasma (electron-positron or electron-ions). Strong electromagnetic fields are generated in the reverse , jet shock and provide an emission site. These magnetic fields contribute to the electron's transverse deflection behind the shock. We have calculated, self-consistently, the radiation from electrons accelerated in the turbulent magnetic fields. We found that the synthetic spectra depend on the Lorentz factor of the jet, its thermal temperature and strength of the generated magnetic fields. The detailed properties of the radiation are important for understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jet shocks, and supernova remnants
A thick, quasi-parallel bow shock structure was observed with field and particle detectors of both HEOS 1 and OGO 5. The typical magnetic pulsation structure was at least 1 to 2 earth radii thick radially and was accompanied by irregular but distinct plasma distributions characteristic of neither the solar wind nor the magnetosheath. Waves constituting the large pulsations were polarized principally in the plane of the nominal shock, therefore also in the plane perpendicular to the average interplanetary field. A separate interpulsation regime detected between bursts of large amplitude oscillations was similar to the upstream wave region magnetically, but was characterized by disturbed plasma flux and enhanced noise around the ion plasma frequency. The shock structure appeared to be largely of an oblique, whistler type, probably complicated by counterstreaming high energy protons. Evidence for firehose instability-based structure was weak at best and probably negative.
A thick quasi-parallel bow shock structure was observed on February 14, 1969, with field and particle detectors of both Heos 1 and Ogo 5. The typical magnetic pulsation structure was at least 1-2 R-E thick radially and was accompanied by irregular but distinct (average) plasma distributions characteristic of neither the solar wind nor the magnetosheath. There appeared to be a separate 'interpulsation' regime occurring between bursts of large amplitude oscillations. This regime was magnetically similar to the upstream wave region but was characterized by disturbed plasma flux and enhanced noise around the ion plasma frequency. The shock structure appeared to be largely of an oblique whistler type, probably complicated by counterstreaming high-energy protons.
Extended Mott-Smith kinetic theory approach to shock wave structure in mixture of two monatomic inert gases
The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.