Showing papers on "Shock wave published in 1971"
TL;DR: In this article, the mean properties of the flow field are established for three types of jet flow issuing from a circular convergent nozzle, and measured distributions of surface pressure are given which result when the jets impinge both normally and obliquely at various distances on several surface shapes.
Abstract: In this, the first part of a two-part experimental study of the behaviour of impinging jets, the mean properties of the flow field are established. Velocity profiles are given for three types of jet flow issuing from a circular convergent nozzle. Measured distributions of surface pressure are given which result when the jets impinge both normally and obliquely at various distances on several surface shapes. The pressure distributions are used to compute the radial velocity gradient at the impingement stagnation point. It is found that for normal impingement this gradient correlates with the free jet centreline velocity and half-radius at the same axial location. A fall-off in the correlated value is noted as the impingement is made oblique. Measurements of the azimuthal distribution of momentum flux in the resulting wall jet are also given. The general behaviour of all three types of jet is found to be similar at locations downstream of any local effects due to the shock waves present in the under-expanded types. A special study of the close-range impingement of an under-expanded jet containing a normal shock disk reveals a region of separated flow surrounding the stagnation point. This condition results in a negative value of the radial velocity gradient at the centreline.
549 citations
01 Jan 1971
TL;DR: In this paper, the authors provide an overview of entropy and shock wave properties of first order partial differential equations in conservation form, and describe all possible entropy conditions of ∂ t U + ∂ x F≦ 0 that can be associated to a given hyperbolic system of two conservation laws.
Abstract: Publisher Summary This chapter provides an overview of shock waves and entropy. It describes systems of the first order partial differential equations in conservation form: ∂ t U + ∂ X F = 0, F = F(u). In many cases, all smooth solutions of the first order partial differential equations in conservation form satisfy an additional conservation law where U is a convex function of u. The chapter discusses that for all weak solutions of ∂ t u j +∂ x f j = 0, j=1,…, m, f j =f j (u 1 ,…, u m ), which are limits of solutions of modifications ∂ t u j +∂ x f j = 0, j=1,…, m, f j =f j (u 1 ,…, u m ) , by the introduction of various kinds of dissipation, satisfy the entropy inequality, that is, ∂ t U + ∂ x F≦ 0. The chapter also explains that for weak solutions, which contain discontinuities of moderate strength, ∂ t U + ∂ x F≦ 0 is equivalent to the usual shock condition involving the number of characteristics impinging on the shock. The chapter also describes all possible entropy conditions of ∂ t U + ∂ x F≦ 0 that can be associated to a given hyperbolic system of two conservation laws.
488 citations
Book•
01 Jan 1971
TL;DR: In this article, a book on shock waves in collisionless plasmas covering basic equations and classification of shock structures, magnetosonic waves, shocks and solitons, electrostatic shocks, etc.
Abstract: Book on shock waves in collisionless plasmas covering basic equations and classification of shock structures, magnetosonic waves, shocks and solitons, electrostatic shocks and solitons, etc
384 citations
01 Jan 1971
TL;DR: In this paper, a book on shock waves in collisionless plasmas covering basic equations and classification of shock structures, magnetosonic waves, shocks and solitons, electrostatic shocks, etc.
Abstract: Book on shock waves in collisionless plasmas covering basic equations and classification of shock structures, magnetosonic waves, shocks and solitons, electrostatic shocks and solitons, etc
371 citations
01 Jan 1971
189 citations
TL;DR: In this article, the authors show that the mid-latitude ionosphere may be in a continual dynamic state if the storms occur sufficiently often and that the density and flux profiles expected during the subsonic phase of the recovery are still not reached after an elapsed time of 10 days and correspondingly there is still a net loss of plasma from the ionosphere to the magnetosphere.
175 citations
174 citations
TL;DR: In this paper, an account of the theory of the light curves of supernovae is presented, based on certain assumptions concerning the passage through the stellar atmosphere of powerful shock waves.
Abstract: An account of the theory of the light curves of supernovae is presented, based on certain assumptions concerning the passage through the stellar atmosphere of powerful shock waves. The investigation is based on numerical integration of appropriate equations of gas dynamics and radiative heat-conductivity. The calculations substantially involve the ionization and recombination of hydrogen in the envelope of a supernova. Changes are traced in the curves arising from the transition from compact stars with small radius (∼10R
⊙), to stars with very extensive envelopes (∼10000R
⊙). The light curves for compact stars agree well with observations of the peculiar supernovae in NGC 5457, NGC 6946 and NGC 5236. The characteristics of the light curves with the passage of shock waves through the extended atmosphere coincide within an order of magnitude with observations of the supernovae of type II and type I near their maximum brightness. A powerful heat-wave propagates before the shock-front in the extensive atmosphere which gives rise to a detached supernova envelope in the form of a thin spherical layer. We investigated the condition in an ascending wave of cooling and recombination in the supernova envelope. It is shown that part of the hydrogen may recombine to attain full transparency for radiation passing through it. The observations are compared with the results of the theory of radioactive decay of the elements. This explanation of the light curves by the passage of shock waves requires energies of 1050 to 1052 ergs, which are in agreement with mechanisms of thermonuclear explosions.
164 citations
TL;DR: In this paper, it was shown that the propagation vector of these wave packets point away from the earth's bow shock and lie between the solar wind flow direction and the average spiral field.
Abstract: One class of waves observed in the interplanetary medium within several earth radii of the earth's bow shock consists of discrete wave packets with amplitudes that are a significant fraction of the background magnetic field. In the spacecraft frame, these wave packets have periods of about 2.5 sec, grow rapidly in time and decay more slowly, and are left-handed with respect to the magnetic field. By using the measured solar wind density and cold plasma dispersion theory, however, we show that these wave packets must be right-handed in the plasma frame at frequencies from about 2 to 4 times the proton gyrofrequency. The propagation vector of these waves is found to point away from the earth's bow shock and to lie between the solar wind flow direction and the average spiral field. The waves are being carried away from the sun by the solar wind, since their velocity is less than the solar wind speed, but they appear to be associated with the intersection of the field line with the earth's bow shock. Since they must be generated in the solar wind plasma, this generation may be caused by the presence of particles streaming upstream from the shock.
155 citations
154 citations
TL;DR: In this article, the least squares technique was applied to combined geomagnetic field and plasma data from a single satellite, assuming Rankine-Hugoniot conservation relations, and the least square technique was used to calculate the shock normal.
Abstract: Shock normal calculation by applying least squares technique to combined geomagnetic field and plasma data from single satellite, assuming Rankine-Hugoniot conservation relations
TL;DR: In this article, a numerical model is presented which describes the evolution with time of a short segment of a spark channel in air and its associated acoustic wave, assuming a straight, cylindrical conducting column in which local thermodynamic equilibrium exists at every point.
Abstract: A numerical model is presented which describes the evolution with time of a short segment of a spark channel in air and its associated acoustic wave. The model assumes a straight, cylindrical conducting column in which local thermodynamic equilibrium exists at every point. The electrical energy input to the column is determined by a prescribed electrical current waveform, coupled with a computation of the plasma conductivity. The evolution with time of the conducting column and its surrounding flow field is then found by numerical integration of the equations of gas dynamics. The model employs a realistic equation of state for air at high temperatures, and incorporates kinetic and radiative energy transport processes. It is shown that a satisfactory description of the properties of a spark channel cannot be achieved when radiative transport processes are neglected. The model agrees well with experimental measurements of spark channel radii, temperatures, pressures, and electron densities, and predicts the resultant shock wave strengths closely. The voltage gradients along the spark channel predicted by the model, and the total energy input to the channel, are not as uniformly in agreement with experiment. Possible reasons for these discrepancies are discussed.
TL;DR: In this paper, a model for the acceleration of the emitting electrons and for the pulsations themselves is presented, which accounts both for the accelerating of the emitted electrons and the pulsation themselves.
Abstract: A CURIOUS but rare feature of the metre–wave continuum (type IV) radiation received from certain large solar flares is the pulsating structure which modulates the intensity in a periodic or quasi-periodic manner1,2. The modulation may persist for about l min or more and the period of the pulsation is typically of the order of 1 s. Of various explanations suggested, we consider the most satisfactory to be that of Rosenberg, in which the radiation is attributed to synchrotron radiation emitted by electrons in a magnetic flux tube embedded in the solar corona and the pulsations are attributed to modulation by standing magnetohydrodynamic (MHD) waves set up within the tube. We now present further evidence of this phenomenon and outline a model which accounts both for the acceleration of the emitting electrons and for the pulsations themselves. There is also evidence to suggest that energetic protons may be accelerated by the same process. We consider that the phenomenon affords a possible observational clue to a physical process by which solar cosmic rays can be generated high in the solar corona.
TL;DR: In this article, forsterite-post spinel phase change was observed at 0.280±0.025 Mb by impacting series of specimens with tungsten alloy plates that are launched at speeds of up to 2.3 km/sec with a high-performance propellant gun.
Abstract: Shock wave data for pure forsterite with initial bulk densities of 2.6 and 3.1 g/cm^3 are obtained to 0.370 Mb by impacting series of specimens with tungsten alloy plates that are launched at speeds of up to 2.3 km/sec with a high-performance propellant gun. The onset of a shock-induced phase change, probably corresponding to the forsterite-‘post spinel’ phase change is observed at 0.280±0.025 Mb. Because of the low shock temperatures, the transition is believed to be limited by the reaction rate and this pressure value should be taken only as an upper limit. Adiabats derived from the Hugoniot data for the forsterite phase are fit to the two-parameter finite strain Birch-Murnaghan equation and to two simple ionic equations of state. The Birch-Murnaghan form of the equation of state gives a zero-pressure bulk modulus (1.29 Mb) that agrees more closely with the ultrasonic data than the modulus obtained from the ionic equations of state. An unusual relaxation effect, in which the elastic shock precursor velocity varies from 5.8 to 9.5 km/sec, is also observed. The characteristic time of the relaxation process appears to be less than 1 μsec.
TL;DR: In this paper, a theory for the production and propagation of the shock wave associated with the supersonic elements of the axial flow compressor is presented, showing that the strength and positions of these shock waves are sensitive to small blade-to-blade differences found in practical builds.
TL;DR: In this paper, the first three waves were taken to be related to the Hugoniot Elastic Limit and to two succeeding polymorphic phase transitions, and scatter in the magnitude of the HEL along the 〈100〉 axis may indicate mixing between the elastic wave and the first phase transition wave.
Abstract: Shock wave experiments with inclined prisms have been used to determine the compression for shocks propagated along three axes of single‐crystal Si. At stresses less than about 200 kbar, the shocks along the 〈110〉 and 〈1111〉 axes exhibited four wave structures. The first three waves were taken to be related to the Hugoniot Elastic Limit and to two succeeding polymorphic phase transitions. Scatter in the magnitude of the HEL along the 〈100〉 axis may indicate mixing between the elastic wave and the first phase transition wave.
TL;DR: In this paper, the laminar wave-train structure of collisionless magnetic slow shocks is investigated using two-fluid hydromagnetics with ion-cyclotron radius dispersion.
Abstract: The laminar wave-train structure of collisionless magnetic slow shocks is investigated using two-fluid hydromagnetics with ion-cyclotron-radius dispersion. For shock strengths less than the maximally strong switch-off shock, in the shock-leading edge, dispersive steepening forms a magnetic-field gradient, while in the downstream flow dispersive propagation forms a trailing wave train; dispersion scale lengths are the ion inerrial length if β > 1 and the ion cyclotron radius if β > 1. In the switch-off slow-shock leading edge, dispersion only produces rotations of the magnetic-field direction; the gradient of the magnetic-field magnitude, and hence the shock-steepening length, is determined solely by resistive diffusion. The switch-off shock structure consists of a long trailing train of magnetic rotations which are gradually damped by resistivity. The low-6 parallel fast switch-on shock has a similar wave-train structure with the magnitude of the field rotations gradually increasing toward the downstream flow.
TL;DR: For example, increases in low energy cosmic ray intensity at front of propagating interplanetary shock waves were observed in this paper, showing that the cosmic ray is more sensitive to the propagation of inter-planetary shocks.
Abstract: Increases in low energy cosmic ray intensity at front of propagating interplanetary shock waves
TL;DR: Probable reverse and forward slow shocks were found in plasma and magnetic-field data from Pioneer 6.2 as discussed by the authors, and the shocks were oblique and weak (Mach of approximately 1.2).
Abstract: Probable reverse and forward slow shocks were found in plasma and magnetic-field data from Pioneer 6. The shocks were oblique and weak (Mach of approximately 1.2). No reverse fast shocks were found. Numerous (50) other discontinuities were found, most of which are probably tangential, since all the plasma parameters changed across most of them.
TL;DR: In this paper, a focused Q-switched ruby laser was used to generate a shock wave at the window-explosive interface when irradiated by a 1000-A-thick aluminum film.
Abstract: Immediate longitudinal detonations have been observed in confined small-diameter columns of PETN, RDX, and tetryl by using a focused Q-switched ruby laser. The energy ranged from 0.8 to 4.0 J in a pulse width of 25 nsec. A 1000-A-thick aluminum film deposited on a glass window was used to generate a shock wave at the window-explosive interface when irradiated by the laser. In some cases, steady-state detonations were reached in less than .5 microsec with less than 10% variation in the detonation velocity.
TL;DR: In this paper, the effects of angular velocity variation on the shock velocity were shown graphically, and it was found that an increase in the initial angular velocity leads to a decrease in the velocity.
Abstract: Similarity solutions describing the flow behind a diverging strong cylindrical shock wave, advancing into a nonuniform gas having solid body rotation, are studied. The effects of the angular velocity variation on the shock velocity are shown graphically. It is found that an increase in the initial angular velocity leads to a decrease in the shock velocity.
TL;DR: In this paper, a simple physical model of fault creep suggests that q = q(k, x, k′), where k is the concentration of dislocations per unit length of fault, x is the position coordinate measured along the fault length, and k′ is the gradient of k. The model suggests that the arrival of these shock waves, which presumably is connected with high earthquake hazard, might be forecast in much the same way as flood crests on river systems are now predicted.
Abstract: The movements of crustal blocks in the new global tectonics can be described in terms of edge dislocations flowing along a transform fault. The dislocations are created at the oceanic ridges and absorbed at the oceanic trenches, but along the transform fault they are conserved. The total creep strain rate across the fault zone at any point on the transform fault will be proportional to q, the flow of dislocations past that point. A simple physical model of fault creep suggests that q = q(k, x, k′), where k is the concentration of dislocations per unit length of fault, x is the position coordinate measured along the fault length, and k′ is the gradient of k. Thus, the flow q is governed by a kinematic wave equation. The propagation of kinematic waves is characterized by amplitude dispersion that leads to the formation of propagating shock waves, i.e. abrupt changes in the creep rate. The model suggests that the arrival of these shock waves, which presumably is connected with high earthquake hazard, might be forecast in much the same way as flood crests on river systems are now predicted. The very large earthquakes along the transform-fault system that bounds the west coast of North America exhibit a migration pattern suggesting kinematic shock propagation. A similar pattern has been observed along the Anatolian fault.
TL;DR: In this article, a hybrid particle-in-cell computer simulation scheme that treats ions as particles and electrons as an isothermal fluid was proposed to deal with the diaphragm problem.
Abstract: Ion‐acoustic shocks in the diaphragm problem are examined with a hybrid particle‐in‐cell computer simulation scheme that treats ions as particles and electrons as an isothermal fluid. Phase space plots and density profiles are given for flows from initial density jumps 1.2≤R = n I /n II ≤15 , with initial temperatures 1≤θ = T e /T iII ≤60 and for times out to ω piII t≤60 , where II denotes the original low‐density conditions. For R = 1.2 , results are in close accord with previous exact linearized solutions. The flows contain nearly antisymmetric compression and expansion regions, with embedded wavelets at θ = 30 , Landau damped away for θ≤5 . New nonlinear features include (a) an increase of the shock Mach number from 1.00 to 1.48, as R = 1.2→15 at θ = 30 , and a constant Mach number ( = 1.20) for R = 3 and variable θ ; (b) a precursor ahead of the θ = 30 fron traveling at 1.60 to 1.80 times the front speed for 1.6≤R≤15 , (c) wash‐out of the wavelets behind the front at large R due to increased Landau damping from heightened T i ; and (d) the intense acceleration of certain region I and II ions into the precursor for low θ(≤10) and large R .
TL;DR: In this paper, the propagation of flare-associated disturbances through the interplanetary medium is examined by using numerical solutions of time-dependent two-dimensional hydrodynamic flow in spherical coordinates.
Abstract: The propagation of flare-associated disturbances through the interplanetary medium is examined by using numerical solutions of time-dependent two-dimensional hydrodynamic flow in spherical coordinates. The study is limited to blast wave phenomena, and the dependence on initial disturbance energy and angular extent is examined. For constant energy disturbances initially occupying cones of half angle up to ∼15° at 0.1 AU, the angular dependence of the transmit time to 1 AU and of the shock shape at 1 AU is very small. For disturbance energies at 0.1 AU of a few times 1030 ergs, transit times to 1 AU are ∼65 hours. The calculated disturbance shapes at 1 AU and the transit times are found to be in good agreement with the observational data.
TL;DR: Suprathermal electron beam induced HF wave instability in solar wind upstream from earth bow shock, interpreting OGO 5 observations as discussed by the authors, interpreted OGO 4 observations and OGO 3 observations...
Abstract: Suprathermal electron beam induced HF wave instability in solar wind upstream from earth bow shock, interpreting OGO 5 observations
TL;DR: In this article, the authors used UV absorption spectroscopy in shock tube studies to study the initiation of hydrogen-oxygen at 1200-1800 K, using UV absorption spectrum.
TL;DR: In this article, it was shown that all of the flow properties within an unsteady shock wave of intermediate strength can be determined by an analysis of the experimentally observed particle trajectories.
Abstract: It is shown that all of the flow properties within an unsteady shock wave of intermediate strength can be determined by an analysis of the experimentally observed particle trajectories. The analysis has been applied to the blast waves from two large trinitrotoluene (t. n. t.) explosions. The particle trajectories were observed by high-speed photography of smoke tracers formed close to the charges immediately before detonation. The density throughout the flow was determined by application of the Lagrangian conservation of mass equation. This was then used to calculate the pressure, assuming adiabatic flow for each air element between shock fronts. The temperature and sound speed throughout the flow were found from the pressure and density, assuming a perfect gas equation of state. The particle velocity within the flow was obtained from the time derivative of the observed particle trajectories. The results have been compared with other blast measurements and with theoretical calculations. It is estimated that the technique gives the flow properties to an accuracy comparable with that for other forms of measurement, namely, 5 to 10%. This is the first time that it has been possible to describe all the properties of a blast wave based on experimental measurements, only.
TL;DR: In this article, the authors observed X-rays diffracted from material which was undergoing shock-wave compression and constructed a film cassette capable of withstanding the effects of the blast with no appreciable destruction of the film.
Abstract: WE have reported1 observing X-rays diffracted from material which was undergoing shock-wave compression. The shock wave was generated by a conventional high-explosive, plane-wave generator. The four-channel scintillation detector used in that experiment2 demonstrated that diffraction had occurred, but it lacked angular resolution. To make this technique practical, a detector system capable of greater resolution had to be devised, and we have recently constructed a film cassette capable of withstanding the effects of the blast with no appreciable destruction of the film.
TL;DR: In this article, the Vlasov equation was used to solve the problem of ion-acoustic collisionless shocks, and the authors showed that different temperature and density ratios produce qualitatively different flows, and they were analyzed in detail.
Abstract: Formation of ion‐acoustic collisionless shocks was studied by numerically solving the one‐dimensional Vlasov equation. The shock propagates at about the local ion‐acoustic speed, and faster than the ion‐acoustic speed ahead; the oscillations behind the shock show ion‐acoustic dispersion. A precursor appears with a speed of 1.6 times the shock speed. Different temperature and density ratios produce qualitatively different flows, and they are analyzed in detail.