Showing papers on "Shock wave published in 1988"

A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter.

Abstract: The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit The shock wave consists of a zero rise time positive spike that falls to 0 at 1 μs followed by a negative pressure component 6 μs long with amplitudes scaled to +1000 and −160 bars, P+ and P−, respectively This pressure wave drives the Gilmore–Akulichev formulation for bubble dynamics; the zero‐order effect of gas diffusion on bubble response is included The negative pressure component of a 1000‐bar shock wave will cause a preexisting bubble in the 1‐ to 10‐μm range to expand to over 100 times its initial size, R0, for 250 μs, with a peak radius of ∼1400 μm, then collapse very violently, emitting far UV or soft x‐ray photons (black body) Gas diffusion does not appreciably mitigate the amplitude of the pressure wave radiated at the primary collapse, but does significantly reduce the collapse temperature Diffusion also increases the bubble radius fro

The sound‐producing oscillations of round underexpanded jets impinging on normal plates

Abstract: The results of acoustical and optical experiments in which ‘‘moderately’’ underexpanded sonic round jets impinge on flat plates normal to the jet axis are presented and analyzed. Periodic unstable oscillations of the jet flow, with the resultant radiation of sound of discrete frequencies, occur over a wide variation of control parameters, namely, pressure ratio, plate size, and spacing of the plate from the jet nozzle. For ‘‘small’’ plates, the principal oscillations with λ/D about 4 (λ=acoustic wavelength, D=nozzle diameter) occur when the standoff shock wave lies in a pressure recovery region of the periodic cellular structure of the choked jet and is, therefore, highly unstable; then the oscillations have key characteristics in common with the high‐harmonic excitation of Hartmann’s acoustic air‐jet generator. An analogous feedback mechanism in the standoff zone is suggested in which pressure waves reflected from the plate trigger the motion of the unstable shock wave. For ‘‘large’’ plates, acoustic fee...

Theory and simulation of collisionless parallel shocks

Abstract: This paper presents a self-consistent theoretical model for collisionless parallel shock structure, based on the hypothesis that shock dissipation and heating can be provided by electromagnetic ion beam-driven instabilities. It is shown that shock formation and plasma heating can result from parallel propagating electromagnetic ion beam-driven instabilities for a wide range of Mach numbers and upstream plasma conditions. The theoretical predictions are compared with recently published observations of quasi-parallel interplanetary shocks. It was found that low Mach number interplanetary shock observations were consistent with the explanation that group-standing waves are providing the dissipation; two high Mach number observations confirmed the theoretically predicted rapid thermalization across the shock.

Magnetic field and density fluctuations at perpendicular supercritical collisionless shocks

Abstract: Perpendicular collisionless shocks are studied by means of two-dimensional hybrid (particle ion, fluid electron) simulations, with emphasis on the relaxation of the highly anisotropic ion distribution that arises primarily from reflection of some of the incident ions but also adiabatic compression of the other, directly transmitted ions and the related growth of low frequency electromagnetic waves. It is commonly assumed that the waves are due to Alfven ion cyclotron instability that propagate parallel to the ambient magnetic field (k/sub perpendicular/ = 0) and that the isotropization of the ions due to pitch angle scattering by the waves and the corresponding modification of the wave spectrum is quasi-linear. It is shown that this is indeed a reasonably good description downstream of the shock front, behind the magnetic overshoot. However, at the shock ramp there is a large discrepancy between the wavelengths measured in the simulations and those predicted by linear theory, and large density and magnetic field oscillations parallel to the ambient magnetic field are also seen. By comparing results for both high and low ion beta cases, it is shown that these effects can be understood in terms of obliquely propagating (k/sub perpendicular/not =0) modes, more likely due to themore » Alfven ion cyclotron instability instead of the (drift) mirror instability, although a more complete explanation awaits the derivation and analysis of an appropriate dispersion relation describing the growth and coupling of low-frequency modes in the inhomogeneous high beta environment of the shock. The observational consequences of these results and their application to improving nonlocal leakage models for the ion foreshock are also discussed. copyright American Geophysical Union 1988« less

Vorticity generation by shock propagation through bubbles in a gas

Abstract: We present a new theoretical model of ‘late-time’ phenomena related to the interaction of a planar shock with a local, discrete inhomogeneity in an ambient gas. The term ‘late-time’ applies to the evolution of the inhomogeneity and the flow field after interaction with the incident shock has ceased. Observations of a shock propagating through a bubble or a spherical flame have exhibited or implied the formation of vortex structures and have showed continual distortion of the bubble or flame. Our theory shows that this is due to the generation of long-lived vorticity at the edge of the discrete inhomogeneity. The vorticity interacts with itself through the medium of the fluid, and, depending on the geometry of the discrete inhomogeneity, can roll up into vortex filaments or vortex rings. To verify and amplify this theoretical description, we use numerical solutions of the fluid equations for conservation of mass, momentum, and energy to study the interaction of a weak shock with a cylindrical or spherical bubble. The simulated bubble has either a higher or lower density than the ambient gas. In this way, the calculations provide insights into the effects of both geometry and distortion of the local sound speed. The Mach number of the shock is 1.2, the ambient gas is air, and the pressure is 1 atmosphere. Because of the simple geometry of each bubble, the vorticity generated at the boundary rolls up into a vortex filament pair (cylindrical bubble) or a vortex ring (spherical bubble). The structural features and timescales of the phenomena observed in the calculations agree closely with recent experiments of Haas & Sturtevant, in which helium and Freon bubbles were used to provide the local departures from ambient density. The discussion of results includes a survey of alternative numerical methods, sources of uncertainty in velocities of interfaces or structures, as derived from the laboratory and numerical experiments, and the relationship of our analysis to other theories.

Electron heating and the potential jump across fast mode shocks

Abstract: Two different methods were applied to determine the cross-shock potential jump in the de Hoffmann-Teller reference frame, using a data set that represented 66 crossings of the terrestrial bow shock and 14 interplanetary shocks observed by various ISEE spacecraft, and one crossing each of the Jovian bow shock and the Uranian bow shock made by the Voyager spacecraft. Results for estimates of the electrostatic potential based on an estimate of the jump in electron enthalpy correlated well with estimates based on Liouville's theorem, although the Liouville-determined values were systematically the higher of the two, suggesting that significant irreversible processes contribute to the shape of the downstream distribution. The potential jump corresponds to approximately 12-15 percent of the incident ion ram kinetic energy, and was found not to be controlled by the Mach number, plasma beta, shock geometry, or electron to ion temperature ratios.

Solitary thermal shock waves and optical damage in optical fibers: the fiber fuse.

Abstract: Fresh experimental and theoretical results on thermally induced catastrophic breakdown (the fiber fuse) in optical fibers are presented, including the observation that the damage is not always irreversible and an analysis of the complex unsteady absorption–heat-conduction process that controls the effect. Good agreement with experiment is obtained with just two independent parameters. The analysis shows that the fiber fuse is a new kind of solitary thermal shock wave in whose leading edge the temperature gradients can reach several thousand kelvins per micrometer.

Shock compression of molten silicate: Results for a model basaltic composition

Abstract: A technique has been developed for measurement of the shock wave, pressure-density equation of state of molten silicates initially at temperatures of up to ∼2000 K. A 40-mm propellant gun apparatus accelerates metal flyer plates to speeds of up to 2.5 km s^(−1); these flyer plates are capable of driving shock waves with amplitudes of 35–40 GPa (350–400 kbar) into molten silicate samples. Modifications to the standard equation of state experiments that are described here include design of a molybdenum sample container for the molten silicate; use of a 10-kW radio frequency induction heater to melt the sample prior to impact; implementation of shuttering systems to protect the optical system and prevent preexposure of the film in the rotating-mirror, continuously writing, streak camera; and reduction of Hugoniot data taking into account the effect of the sample capsule. Data for a model basaltic liquid (36 mol % anorthite, 64 mol % diopside) at an initial temperature of 1673 K and initial density of 2.61 Mg m^(−3), yield a shock velocity-particle velocity (U_(S)-U_(P)) relation given by U_S = 3.06 + 1.36 UP km s^(−1) up to values of U_P = 1.7 km s^(−1). The zero-pressure, bulk sound speed is in good agreement with ultrasonic measurements. The best fit Birch-Murnaghan equation of state for this model basaltic liquid is K_(0S) = 24.2 GPa and K′ = 4.85 based on Hugoniot points at low pressures (<25 GPa). Within the resolution of our data set, density increases smoothly with pressure over the 0–25 GPa pressure range, suggesting that structural rearrangements take place gradually in response to pressure in this pressure interval. At high pressures (≳ 25 GPa) the Hugoniot data suggest that the liquid stiffens considerably. This may indicate that the gradual structural changes characteristic of the lower-pressure regime, such as changes of Al3+ and Si4+ coordination by oxygen from fourfold to sixfold, are essentially complete by ∼25 GPa. These high-pressure Hugoniot data are fit by US = 0.85 + 2.63 Up km s^(−1). The high-pressure regime is similar to that obtained in initially solid silicates upon shock compression. Shock temperature calculations yield values of 2400–2600 K at 25 GPa, and the states achieved are believed to lie metastably in the liquid field.

A study of the collapse of arrays of cavities

Abstract: This paper describes a method for examining the collapse of arrays of cavities using high-speed photography and the results show a variety of different collapse mechanisms. A two-dimensional impact geometry is used to enable processes occurring inside the cavities such as jet motion, as well as the movement of the liquid around the cavities, to be observed. The cavity arrangements are produced by first casting water/gelatine sheets and then forming circular holes, or other desired shapes, in the gelatine layer. The gelatine layer is placed between two thick glass blocks and the array of cavities is then collapsed by a shock wave, visualized using schlieren photography and produced from an impacting projectile. A major advantage of the technique is that cavity size, shape, spacing and number can be accurately controlled. Furthermore, the shape of the shock wave and also its orientation relative to the cavities can be varied. The results are compared with proposed interaction mechanisms for the collapse of pairs of cavities, rows of cavities and clusters of cavities. Shocks of kbar (0.1 GPa) strength produced jets of c. 400 m s−1 velocity in millimetre-sized cavities. In closely-spaced cavities multiple jets were observed. With cavity clusters, the collapse proceeded step by step with pressure waves from one collapsed row then collapsing the next row of cavities. With some geometries this leads to pressure amplification. Jet production by the shock collapse of cavities is suggested as a major mechanism for cavitation damage.

A mechanism for strong shock electron heating in supernova remnants

Abstract: It is shown that collisionless shock waves propagating away from a supernova may be directly responsible for the 10 keV X-ray emission seen in supernova remnants. A sequence of plasma instabilities (Buneman and ion acoustic) between the reflected and/or transmitted ions and the background electrons at the foot of the shock front can give rise to rapid anomalous heating of electrons. Hybrid simulations of a perpendicular collisionless shock are presented to demonstrate that this heating can arise within a self-consistently computed shock structure.

Maximum Energy of Cosmic-Ray Particles Accelerated by Supernova Remnant Shocks in Stellar Wind Cavities

Abstract: Diffusive shock acceleration, balanced by adiabatic losses, leads readily to particle energies of more than 10 to the 15th eV in the case of a supernova shock freely expanding into a stellar wind cavity. This process accelerates particles early on out of stellar wind material which is often enriched in certain elements (isotopes), and may thus contribute to explain elemental and isotopic anomalies in the cosmic rays. It is speculated that the same process may produce particle energies up to 10 to the 19th eV in the case of a supernova explosion in a compact binary star. 22 references.

Biological effects of shock waves: kidney haemorrhage by shock waves in dogs--administration rate dependence.

Abstract: The effect of shock waves on normal canine kidneys was examined in two groups of dogs whose right kidneys were exposed to 3000 shock waves generated with 20 kV and 40 nF in a Dornier HM II lithotripter The groups differed only in the rate of shock wave administration which was 100 and 1 per second, respectively Autopsy was performed 24 to 30 h later Macroscopically and histologically, significantly more haemorrhages occurred in the kidney parenchyma if shock waves were administered at a rate of 100 waves per second Haemorrhages were diffuse, the outer medulla was most heavily affected The results show that kidney damage is dependent on the rate of shock wave administration They argue against a direct shock wave effect and favor cavitation as the mechanism of shock wave damage although thermal effects cannot be excluded

Ultrasound or shock wave work process and preparation for carrying out same

Abstract: The invention relates to a shock wave or ultrasound work process wherein shock wave or ultrasound generators are used to produce shock waves or ultrasound in a medium in which an effect is to be achieved, wherein to this medium is added a preparation which contains or produces microbubbles which cause an intensification of the shock wave or ultrasound effect, and to a preparation for carrying out the process wherein this preparation can also be used for the specific destruction of biological tissue with ultrasound and shock waves.

Gas compression and jet formation in cavities collapsed by a shock wave

Abstract: A range of techniques, including high-speed photography and image intensification, are used to study the collapse of cavities by shock waves. Of particular interest are the shape changes of the cavity and the production of luminescence at 'hot spots' in the gas. The relevance of the research to cavitation damage, explosive initiation, and medical uses of acoustic waves is discussed.

On the origin of hot diamagnetic cavities near the Earth's bow shock

Abstract: The origin of hot diamagnetic cavities (HDCs) observed occasionally upstream from the earth's bow shock is investigated by examining the results of November 16, 1977, observation, when four of these events occurred on a single day, as well as plasma and field data from that day. The results suggest that HDCs may form as a result of an unusually strong interaction between shock-reflected ions and the incoming solar wind. It is proposed that this interaction stems from a temporary and localized reflection of a larger-than-normal fraction of the incident ions, which is stimulated by sudden changes in the upstream field orientation; the consequences of such a temporary overreflection are found to be consistent with many of the observed features of HDCs, including the strong slowing, deflection, and heating of the flow, as well as the localization, internal recoveries, and occasional formation upstream from the shock itself.

Three-dimensional plasma structures with anomalous flow directions near the Earth's bow shock

Abstract: We have examined AMPTE IRM data obtained in the solar wind near the Earth's bow shock and found 16 well-defined cases where a region of hot subsonic plasma is embedded in the solar wind Such structures had been observed first with instruments on ISEE 1 and 2 and later on AMPTE UKS and distinguished from bow shock crossings Our observations confirm some of the earlier findings, notably the event profile, showing a hot, low-density core flanked by narrow regions of high density and strong magnetic field We also find the low (∼200 km/s) flow velocities, strongly deflected from the solar wind, and we substantially strengthen the local time dependence of the flow which invariably is directed dawnward for prenoon events and duskward for postnoon events Our results differ from the reported ISEE results in two respects First, the flows we observe tend to have larger angles relative to the solar wind, and they often even have a sunward component Second, the events we have selected cannot be described as diamagnetic cavities On the contrary, the magnetic fields are usually significantly enhanced This apparent discrepancy may simply result from different event selection criteria A quantitative analysis of the regions flanking the hot core shows they consist of fast, nearly perpendicular, supercritical shocks on the outside and tangential discontinuities on the inside We find a systematic difference between the orientations of the leading and trailing edge boundary normals While the former are directed largely transverse to the solar wind flow, the latter are more nearly aligned with the solar wind Another new finding concerns the presence of enhanced fluxes of >70-keV electrons which appear to be of magnetospheric origin The majority of events are associated with directional discontinuities in the interplanetary magnetic field We have also found events which are not embedded in the solar wind but occur between the solar wind and the magnetosheath, at times replacing the regular bow shock Among the mechanisms discussed as causes for these events are the formation of sunward directed plasma jets from magnetopause reconnection, or from amplification of magnetic stresses associated with rotational discontinuities in the interplanetary medium; sudden and localized enhancements of bow shock reflection; and the interaction of the bow shock with tangential discontinuities having a specific internal structure

High‐speed photography of surface geometry effects in liquid/solid impact

Abstract: Recent theoretical studies of liquid/solid impact, in particular the geometric wave theory of Lesser and Field, have emphasized the importance of the detailed geometry in the contact area. In parallel with the theoretical work, we have developed a two‐dimensional technique using gels for impact and shock studies. A combination of high‐speed photography and schlieren optics allows the shocks in the liquid and solid, if it is transparent, to be visualized, as well as important processes, such as jetting, to be recorded. This paper describes the gel technique and gives results for a range of surface geometries for collision velocities of a few hundred meters per second. The relevance to damage initiation in liquid/solid impact problems, such as rain erosion, steam turbine blade erosion, and cavitation, are discussed.

Modeling shock-wave deformation via molecular dynamics

Abstract: Molecular dynamics (MD), where the equations of motion of up to thousands of interacting atoms are solved on the computer, has proven to be a powerful tool for investigating a wide variety of nonequilibrium processes from the atomistic viewpoint. Simulations of shock waves in three-dimensional (3D) solids and fluids have shown conclusively that shear-stress relaxation is achieved through atomic rearrangement. In the case of fluids, the transverse motion is viscous, and the constitutive model of Navier-Stokes hydrodynamics has been shown to be accurate---even on the time and distance scales of MD experiments. For strong shocks in solids, the plastic flow that leads to shear-stress relaxation in MD is highly localized near the shock front, involving slippage along close-packed planes. For shocks of intermediate strength, MD calculations exhibit an elastic precursor running out in front of the steady plastic wave, where slippage similar in character to that in the very strong shocks leads to shear-stress relaxation. An interesting correlation between the maximum shear stress and the Hugoniot pressure jump is observed for both 3D solid and fluid shock-wave calculations, which may have some utility in modeling applications. At low shock strengths, the MD simulations show only elastic compression, with no permanent transverse atomic strains. This result for perfect 3D crystals is also seen in calculations for 1D chains. We speculate that, if it were practical, a very large MD system containing dislocations could be expected to exhibit more realistic plastic flow for weak shock waves too.

Active current sheets near the Earth's bow shock

Abstract: We present here an investigation of “active current sheets” observed by the AMPTE UK spacecraft near the Earth's bow shock, concentrating on their macroscopic features and geometry. Events selected primarily by flow directions which deviate substantially from the Sun-Earth line show similar characteristics, including their association with an underlying macroscopic current sheet and a hot central region whose flow direction is organized, at least in part, by location relative to the inferred initial intersection point between the current sheet and the bow shock. This region is flanked by “edges” which, according to a Rankine-Hugoniot analysis, are often fast shocks whose orientation is consistent with that expected if a “bulge” on the bow shock convected past the spacecraft. We have found the magnetosheath manifestations of these events which we study in detail. We suggest that these events are the direct result of the disruption and reformation of the bow shock by the passage of an interplanetary current sheet, most probably a tangential discontinuity.

Acceleration of cosmic rays by shock waves

Abstract: Theoretical work on various processes by which shock waves accelerate cosmic rays is reviewed. The most efficient of these processes, Fermi acceleration, is singled out for special attention. A linear theory for this process is presented. The results found on the basis of nonlinear models of Fermi acceleration, which incorporate the modification of the structure caused by the accelerated particles, are reported. There is a discussion of various possibilities for explaining the generation of high-energy particles observed in interplanetary and interstellar space on the basis of a Fermi acceleration mechanism. The acceleration by shock waves from supernova explosions is discussed as a possible source of galactic cosmic rays. The most important unresolved questions in the theory of acceleration of charged particles by shock waves are pointed out.

Research in Applied Mathematics.

Abstract: : Most of the work has been on shock dynamics, a term we use for problems of the focusing of curved shocks, the diffraction of shocks by bodies or density layers, the propagation of shocks down curved tubes and channels, and the stability of converging shocks. Our earlier theoretical work is described in the book Linear and Nonlinear by G.B. Whitham, and references given there. This theoretical work on shock dynamics had been found by experimenters to be extremely useful in practical situations. However, the analytic results had been limited to fairly simple situations. The numerical scheme originally proposed was again limited and could not hope to handle some of the interesting practical situations. Keywords: Shock waves, Solitons, Roll waves; Nonlinear wave propagation; Numerical methods.

Time-resolved investigations of laser-induced shock waves in water by use of polyvinylidenefluoride hydrophones

Abstract: Laser light from a Q‐switched Nd:yttrium‐aluminum‐garnet laser (λ=1064 nm; pulse duration=20 ns; pulse energies up to 150 mJ) focused into water creates shock waves by rapidly expanding microplasmas. Using piezoelectric, thin‐film polyvinylidenefluoride (PVDF) as a transducer, a broadband hydrophone (100‐MHz bandwidth) was developed to investigate underwater shock waves. The electrical signal is analyzed with respect to reflections of the shock wave within the transducer and the input impedance of the measuring device. The shock waveform is determined, its peak pressure ranging to kbars (108 Pa), decreasing with r−1.12 and increases by the square root of the laser pulse energy. The time resolution of the hydrophone (4 ns) is sufficient to determine the plasma dimensions and the number of shock waves generated by a single laserpulse. Both vary statistically, primarily because of contaminations in the fluid. Because of the length of the region containing plasmas, different peak pressures are found in the di...

Modeling two-dimensional detonations with detonation shock dynamics

Abstract: One of the principal shortcomings of the computer models that are presently used for two‐dimensional explosive engineering design is their inadequate treatment of the explosive’s detonation reaction zone. Current methods lack the resolution to both calculate the broad gas expansion region and model the thin reaction zone with reasonable detail. Recently an alternative method for modeling the reaction zone has been developed. This method applies when the radius of curvature of the shock is large compared to the reaction‐zone length. In this limit, the dynamics of the interaction between the chemical heat release and the two‐dimensional flow in the reaction zone is quasisteady. It is summarized by a relation Dn(κ), between the local normal shock velocity Dn and shock curvature κ. When this relation is combined with the kinematic surface condition (an equation that describes how disturbances move along the shock), the two‐dimensional reaction‐zone calculation is reduced to a one‐dimensional calculation.

Propagation of weak shocks through a random medium

Abstract: The propagation of weak shock waves (M_s = 1.007, 1.03 and 1.1) through a statistically uniform random medium has been investigated experimentally in a shock tube. The wave-from geometry, rise time and amplitude of initially plane shocks which have propagated through a random mixture of helium and refrigerant 12 are measured. The effect of shock propagation on the properties of the random medium is visualized with schlieren and shadow photography. The pressure histories of the distorted shock waves reflecting from a normal end wall are observed to be both peaked and rounded. In the rounded case the perturbed shock is found to be made up of a succession of weak, slightly curved fronts with a total effective rise time orders of magnitude greater than the classical Taylor thickness. The radius of curvature of the weakest shocks after propagating through the random medium is inferred from observations at two downstream stations to be about 7 times the integral scale of the gas inhomogeneities. It is concluded that the observed distortions of the wave fronts can best be explained in terms of random focusing and defocusing of the front by the inhomogeneities in the medium. A ray-tracing calculation has been used to interpret the experimental observations. It is found that geometrical considerations are sufficient to account for many of the effects observed on the shocks.

The MHD intermediate shock interaction with an intermediate wave: Are intermediate shocks physical?

Abstract: Contrary to the usual belief that MHD intermediate shocks are extraneous, we have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. In this paper, we clarify the differences between the conventional view and our results by studying the interaction of an MHD intermediate shock with an intermediate wave. The study reaffirms our results. In addition, the study shows that there exists a larger class of shocklike solutions in the time-dependent dissipative MHD equations than are given by the MHD Rankine-Hugoniot relations. It also suggests a mechanism for forming rotational discontinuities through the interaction of an intermediate shock with an intermediate wave. The results are of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models.

Shock waves in water

Abstract: The present paper gives a comprehensive examination of equations and charts for shock waves in water. The Tait equation of state is used in the analysis to describe the compressibility of water. The results for an oblique shock wave are presented in the hodograph plane where all possible velocity vectors downstream of the shock wave are seen to lay on a single curve (i.e., shock polar). The equation of the shock polar and the corresponding charts up to upstream Mach number of 3 are given, as well as a more convenient way of adapting the shock polar. The oblique shock‐wave detachment condition and the sonic flow condition downstream of a shock are also presented.

Discovery of the bow shock of Cygnus A

Abstract: Rotation measure images of Cygnus A indicate that a bow shock precedes the supersonic advance of hot spot B into the intergalactic medium (IGM). The shock is radio quiet and is observed only by the rotation measure discontinuity which occurs at the point where the fields and particles in the IGM are compressed by the shock. The fact that this discontinuity is projected onto part of the source provides information on the three-dimensional structure of the radio source and supports models of extragalactic radio sources in which the jet varies direction on relatively short time scales. From the observed rotation measures, magnetic field strengths in the cluster gas are calculated at about 7.5 microG. 22 references.

Effects of dissipation on rotational discontinuities

Abstract: The effects of dissipation on rotational discontinuities have been studied as an initial-value problem. Starting with a rotational discontinuity, the author applies resistivity and viscosity and follows the resulting evolution of the system by numerically integrating in time the viscous, resistive MHD equations. The results show that by including dissipation, a rotational discontinuity is unstable and will evolve to an MHD intermediate shock of the kind whose shock frame fluid velocities are subfast, super-Alfvenic, and superslow ahead, and subfast, sub-Alfvenic, and superslow behind the shock. (However, with small dissipation, the intermediate shock and the rotational discontinuity would be very close.) The results also show that there are a larger class of shocklike structures, which do not satisfy Rankine-Hugoniot relations, in the time-dependent dissipative MHD equations. The results also indicate that the corresponding Riemann problem is not well-posed. in addition, the admissibility of MHD equations is discussed. The conclusion is that all entropy satisfying shocks along the shock curve are physical. This differs from the conventional view that intermediate shocks are not allowed. This also differs from the admissibility criterion of Oleinik (1957) and Liu (1981). However, their criterion is valid for a strictly hyperbolic system, whereas the set of MHDmore » equations is nonstrictly hyperbolic. Regarding the magnetospheric physics, the study suggests that instead of rotational discontinuities, intermediate shocks should exist at the magnetopause. Thus one has a different signature from that of a rotational discontinuity to compare with space observations.« less