Kinds Of Shock Waves Research Articles

Simple dynamical model that leads to sputter cone formation.

We introduce a model for sputter cone formation that includes only the angular dependence of the sputter yield and a fourth-order smoothing effect like surface diffusion. In one dimension, a sputter cone is a particular kind of shock wave that is known as an undercompressive shock. Simulations of our model show that a wide variety of initial conditions lead to the formation of sputter cones and that the opening angle of the cones does not depend on the detailed form of the initial condition. In two dimensions, a sputter cone is a higher-dimensional analog of an undercompressive shock. For two particularly simple choices of parameters, a sputter cone is a four-sided pyramid with rounded edges that is produced by the superposition of two orthogonal, one-dimensional undercompressive shocks.

Ion Acoustic Shocks in a Weakly Relativistic Ion-Beam Degenerate Magnetoplasma

A theoretical investigation is carried out to study the propagation properties of ion acoustic shocks in a plasma comprising of positive inertial ions, weakly relativistic ion beam and trapped electrons in the presence of a quantizing magnetic field. By using the reductive perturbation technique, the Korteweg–de Vries-Burgers (KdVB) equation and oscillatory shocks solution are derived. The characteristics of such kinds of shock waves are examined and discussed in detail under suitable conditions for different physical parameters. The strength of the magnetic field, ion beam concentration and ion-beam streaming velocity have a great influence on the amplitude and width of the shock waves and oscillatory shocks. The results may be useful to study the characteristics of ion acoustic shock waves in dense astrophysical regions such as neutron stars.

Scaling spray penetration at supersonic conditions through shockwave analysis

In the current paper, an investigation of the supersonic flow effect on shockwave generation and diesel spray penetration scaling has been performed. For this purpose, spray visualization tests have been carried out in a constant-pressure chamber at room temperature using shadowgraphy technique. Two working gases have been used: nitrogen, with similar thermodynamic characteristics to the engine environment, and sulfur hexafluoride, aimed at producing supersonic conditions at moderate injection pressure values. A total of 60 operating points, including different nozzle geometries, injection pressures and chamber densities have been studied. From the visualization study, two different kinds of shockwaves have been detected: normal or frontal, for moderate spray tip Mach (between 1 and 1.5); and oblique, when the Mach is higher than 1.5. The penetration results show that, for the same injection conditions in terms of injection pressure and chamber density, the spray propagation is equal for SF6 and N2 when the spray is on subsonic conditions, while penetration is higher for SF6 when supersonic velocity is reached. This behavior has been related to the density gradient appearing across the shockwave. A new methodology to extrapolate supersonic penetration from the well-known subsonic penetration law has been proposed, showing good agreement with the experimental results.

Formation of shocks related to dust-particle charging in complex plasmas

The nonstationary problem of the evolution of perturbation and its transformation into nonlinear wave structure in complex plasmas (multicomponent plasmas containing ions, electrons, charged microspheres or dust grains, and neutral gas) is considered. For this purpose, the model, which takes into account the variation of ion density and the ion-momentum dissipation due to dust-particle charging, as well as the source of plasma particles due to the ionization process, is developed. The model is appropriate for the description of laboratory experiments in complex plasmas and contains all basic mechanisms responsible for the formation of a new kind of shock waves which is related to the anomalous dissipation due to the dust-particle charging process. The consideration on the basis of this model allows us to obtain shock structures as a result of evolution of an initial perturbation and to explain the experimental value of the width of the ion acoustic shock-wave front, as well as the shock-wave speed. The solution of the problem of the evolution of perturbation and its transformation into a shock wave in complex plasmas opens up possibilities for description of the real phenomena like supernova explosions, as well as of the laboratory and active space and geophysical experiments.

Shocks In Space Dusty Plasmas

An anomalous dissipation originating from the dust particle charging processes results in a possibility of existence of a new kind of shock waves in a dusty plasma. The shock waves related to this dissipation can be important for description of star formation, shocks in supernova explosions, particle acceleration in shocks, etc. The hydrodynamical description of shock waves in space dusty plasmas is presented. The possibility of the experimental study of the shock waves related to the dust charging process in active space experiments in the Earth's magnetosphere is discussed.

Electron acceleration and type II radio emission at quasi-parallel shock waves

Solar type II radio bursts are interpreted as the radio signature of shock waves travelling through the solar corona. Some of these shock waves are able to enter into the interplanetary medium and are observed as interplanetary type II bursts. The nonthermal radio emission of these bursts indicates that electrons are accelerated up to superthermal and/or relativistic velocities at the corresponding shocks. Plasma wave measurements at interplanetary shock waves support the assumption that the fundamental type II radio emission is generated by wave-wave interactions of electron plasma waves and ion acoustic waves and that the source region is located near the transition region of the shock. Therefore, the instantaneous bandwidth of type II bursts should reflect the density jump across the shock. Comparing the theoretically predicted density jump of coronal shock waves (Rankine-Hugoniot relations) and the measured instantaneous bandwidth of solar type II radio bursts it is appropriate to assume that these bursts are generated by weak supercritical quasi-parallel shock waves. Two different mechanisms for the accelaration of electrons at this kind of shock waves are investigated in the form of test particle calculations in given magnetic and electric fields. These fields have been extracted from in-situ measurements at the quasi-parallel region at Earth’s bow shock, which showed large amplitude magnetic field fluctuations (so-called SLAMS: Short Large Amplitude Magnetic Field Structures) as constituent parts. The first mechanism treats these structures as strong magnetic mirrors, at which charged particles are reflected and accelerated. Thus, thermal electrons gain energy due to multiple reflections between two approaching SLAMS. The second mechanism shows that it is possible to accelerate electrons inside a single SLAMS due to a noncoplanar component of the magnetic field in these structures. Both mechanism are described in the form of test particle calculations, which are supplemented by calculations according to adiabatic theory. The results are discussed for circumstances in the solar corona and in interplanetary space.

Shock Structures in Plasmas Containing Variable-Charge Macro Particles

The results on shock waves in plasmas containing variable-charge dust grains are reviewed. The problems where the shock waves in dusty plasmas can be important are formulated. The dusty plasma is presented as an open, highly dissipative system where there is a tendency to self-organization. An anomalous dissipation originating from the charging processes results in a possibility of existence of a new kind of shock waves. The shock waves related to this dissipation can be important for description of star formation, shocks in supernova explosions, particle acceleration in shocks, formation of dusty crystals, etc.

101 薄膜センサーを用いた物体回りの高速流れの計測(その2)

In the super sonic flow through the cascade of a gas-turbine engine, flow separation and shock waves are important phenomena impacting the performance. In previous report1) flow separation can be detected using hot film sensors. And we show the possibility that shock waves can be detected using these sensors. This report describe additional experiment to improve the detection of shock waves. In super sonic wind tunnel test, two kinds of shock waves, that are differed in strength, are indused to occur on the surface of the cone-like models at Mach 2.5. Data are collected from hot film sensors located on the surface. Schlieren flow visualization method is also applied to check the flow. As the results, the shock wave can be detected by the differences between the sensor output.

Geostrophic Shock Waves

Abstract Organized depth discontinuities involving a balance between steepening and dissipation are usually referred to as shock waves. An analytical “educed gravity” model is used to examine a special kind of shock wave. The wave under study is a depth discontinuity associated with a transition between a supercritical and subcritical flow in a channel. Even though the wave itself is highly nonlinear, the adjacent upstream and downstream fields are exactly geostrophic in the cross-stream direction. For this reason we term the wave a geostrophic shock wave. We focus on a stationary shock wave whose horizontal projection is a straight line perpendicular to the side walls. Solutions for the entire field are constructed analytically using power series expansions and shock conditions equivalent to the so-called Rankine-Hugoniot constraints. It is found that, for particular upstream conditions, a geostrophic shock wave can be formed if the particle speed exceeds the surface gravity wave speed (i.e., the flow is...

Comments on the existence of a cylindrical-symmetric relativistic shock wave with an azimuthal magnetic field

In the paper cited below, the boundary conditions in front of the shock do not satisfy the basic equation. Therefore, the existence of this kind of shock wave is impossible.

Magneto-Fluid Dynamic Shock Waves

A discussion is given on the structure of hydromagnetic shock waves where the collision frequency is very low compared to the gyrofrequency of the ions or electrons. Three problems are discussed: the general properties of the shock waves and the influence of the magnetic field; the thickness of the shock wave; and which of the various kinds of shock waves can occur and which do develop, if an initial perturbation is given. (B.O.G.)

Instationäre Stoßfronten und ihre Wechselwirkung

A summarizing and critical report is given (containing 10 published and 5 unpublished papers) about a teamwork, leaded by v. Weizsäcker, on shock waves and their interactions. The aim of this team was to prepare the way for a theory of supersonic turbulence, which is strongly needed in astrophysics. The following results have been reached: 1 Let a single, plain, strong shock wave propagate into a gas of uniform density and velocity. Under the single condition that no large supply of momentum is pushing from behind, all initial distributions (of density, velocity and temperature behind the front) reach after a short time asymptotically the same distribution which is called the “standard solution”. It is time-independent apart from its scale factors. 2 This standard solution has been identified with a homology solution with a critical value k0 of the homology parameter k, while all values other than k0 lead to singularities of density or temperature at finite distances. Some attemps have been made to prove the stability of this solution. 3 In the standard solution as well as in many other hydrodynamical problems we get velocity distributions which are almost linear with distance. Thus the class of linear solutions of the Eulerian equations has been investigated. 4 The loss of energy by radiation has been calculated, the results are applied to cosmical data. In the limiting case of very strong radiation, we get the instationary “isothermal shock wave”. There may exist an isothermal standard solution too, but it cannot be time-independent. 5 Shock waves of all strengths in magnetic fields of all strengths and all directions have been treated. There seems to exist three different kinds of shock waves. 6 Some examples have been calculated to the interaction of two instationary, parallel, strong shock waves, showing the resulting distributions and their time-development. 7 In a preliminary way, a field of interacting shock waves (of various velocities and lengths) has been treated by Monte-Carlo-method, in order to show how a state of equilibrium might be set up and in which statistical terms it can be described.