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1.
Similarity solutions are obtained for spherical radiation-driven shock waves propagating in a non-uniform atmosphere at rest obeying a density power law. Approximate analytical solutions are also obtained and found to be in good agreement with the numerical solutions. The effect of the parameter characterizing the initial density distribution of the gas on solutions of the flow field is studied in detail. It is also shown analytically that the shock wave propagates as an overdriven detonation.  相似文献   

2.
We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, p , and energy density, μ, in the shock-heated matter are assumed to obey   p = w μ  , where w is a positive constant. Consistent solutions are found for shocks propagating from the symmetry centre of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy density at the shock, a black hole is avoided altogether and the solutions are regular at the centre. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy density. We also discuss self-similar solutions without shocks in fluids with   w < −1/3  .  相似文献   

3.
R. E. Grundy 《Solar physics》1975,40(1):227-230
This paper deals with shock conditions for the progressing wave (or similarity) solutions of one-dimensional, unsteady gas dynamics. These solutions have hitherto been used to deal with the flow behind shocks moving into stationary atmospheres. By generalising the shock conditions to the case of moving atmospheres, it is shown that the progressing wave solutions can be used to describe a certain class of flows, and a new shock locus can be constructed in the phase plane of the solutions. It is hoped that such solutions will be of use in describing the unsteady flow behind shocks propagating into the ambient solar wind.  相似文献   

4.
Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.  相似文献   

5.
Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas,which has a variable azimuthal and axial fluid velocity.The dusty gas is assumed to be a mixture of small solid particles and perfect gas.The equilibrium flow conditions are assumed to be maintained,and the density of the mixture is assumed to be varying and obeying an exponential law.The fluid velocities in the ambient medium are assumed to obey exponential laws.The shock wave moves with variable velocity.The effects of variation of the mass concentration of solid particles in the mixture,and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times.Also,a comparison between the solutions in the cases of isothermal and adiabatic flows is made.  相似文献   

6.
We explore the global structure of the accretion flow around a Schwarzschild black hole where the accretion disc is threaded by toroidal magnetic fields. The accretion flow is optically thin and advection dominated. The synchrotron radiation is considered to be the active cooling mechanism in the flow. With this, we obtain the global transonic accretion solutions and show that centrifugal barrier in the rotating magnetized accretion flow causes a discontinuous transition of the flow variables in the form of shock waves. The shock properties and the dynamics of the post-shock corona are affected by the flow parameters such as viscosity, cooling rate and strength of the magnetic fields. The shock properties are investigated against these flow parameters. We further show that for a given set of boundary parameters at the outer edge of the disc, accretion flow around a black hole admits shock when the flow parameters are tuned for a considerable range.  相似文献   

7.
We performed shock recovery experiments on an olivine‐phyric basalt at shock pressures of 22.2–48.5 GPa to compare with shock features in Martian meteorites (RBT 04261 and NWA 1950). Highly shocked olivine in the recovered basalt at 39.5 and 48.5 GPa shows shock‐induced planar deformation features (PDFs) composed of abundant streaks of defects. Similar PDFs were observed in olivine in RBT 04261 and NWA 1950 while those in NWA 1950 were composed of amorphous lamellae. Based on the present results and previous studies, the width and the abundance of lamellar fine‐structures increased with raising shock pressure. Therefore, these features could be used as shock pressure indicators while the estimated pressures may be lower limits due to no information of temperature dependence. For Martian meteorites that experienced heavy shocks, the minimum peak shock pressures of RBT 04261 and NWA 1950 are estimated to be 39.5–48.5 GPa and 48.5–56 GPa, respectively, which are found consistent with those estimated by postshock temperatures expected by the presence of brown olivine. We also investigated shock‐recovered basalts preheated at 750 and 800 °C in order to check the temperature effects on shock features. The results indicate a reduction in vitrifying pressure of plagioclase and a pressure increase for PDFs formation in olivine. Further temperature‐controlled shock recovery experiments will provide us better constraints to understand and to characterize various features found in natural shock events.  相似文献   

8.
We describe similarity solutions that characterize the collapse of collisional gas on to scale-free perturbations in an Einstein–de Sitter universe. We consider the effects of radiative cooling and derive self-similar solutions under the assumption that the cooling function is a power law of density and temperature, Λ( T , ρ )∝ ρ 3/2 T . We use these results to test the ability of smooth particle hydrodynamics (SPH) techniques to follow the collapse and accretion of shocked, rapidly cooling gas in a cosmological context. Our SPH code reproduces the analytical results very well in cases that include or exclude radiative cooling. No substantial deviations from the predicted central mass accretion rates or from the temperature, density and velocity profiles are observed in well-resolved regions inside the shock radius. This test problem lends support to the reliability of SPH techniques to model the complex process of galaxy formation.  相似文献   

9.
Similarity solutions describing the flow of a perfect gas behind a cylindrical shock wave with transverse magnetic field are investigated in an inhomogeneous medium. The total energy of the shock wave is assumed to be constant. A comparative study has been made between the results with and without magnetic field.  相似文献   

10.
Standing, propagating or oscillating shock waves are common in accretion and winds around compact objects. We study the topology of all possible solutions using the pseudo-Kerr geometry. We present the parameter space spanned by the specific energy and angular momentum and compare it with that obtained from the full general relativity to show that the potential can work satisfactorily in fluid dynamics also, provided the polytropic index is suitably modified. We then divide the parameter space depending on the nature of the solution topology. We specifically study the nature of the standing Rankine–Hugoniot shocks. We also show that as the Kerr parameter is increased, the shock location generally moves closer to the black hole. In future, these solutions can be used as guidelines to test numerical simulations around compact objects.  相似文献   

11.
This paper presents global solutions of adiabatic accretion flows with isothermal shocks in Kerr black hole geometry. It is known that in the previously studied cases, where the flow including the shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of α –x type. However, the solution topology in the present case shows remarkable new characteristics: for the same flow parameters there can be two stable shock solutions satisfying physical boundary conditions, and the solution can be of three types, namely α– x , x –α and α–α type. In addition, shocks in the present case occur for a parameter region different from that for Rankine–Hugoniot shocks. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also significant that the effects of frame-dragging of a rapid Kerr black hole on the shock formation are discovered. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flows, namely those of Shakura & Sunyaev and Narayan & Yi, and some comments are made about the fact that numerous authors who have studied transonic global solutions of accretion flows have found no shocks.  相似文献   

12.
We model a one-dimensional shock-tube using smoothed particle hydrodynamics and investigate the consequences of having finite shock-width in numerical simulations caused by finite resolution of the codes. We investigate the cooling of gas during passage through the shock for three different cooling regimes.
For a theoretical shock temperature of 105 K, the maximum temperature of the gas is much reduced. When the ratio of the cooling time to shock-crossing time was 8, we found a reduction of 25 per cent in the maximum temperature reached by the gas. When the ratio was reduced to 1.2, the maximum temperature reached dropped to 50 per cent of the theoretical value. In both cases the cooling time was reduced by a factor of 2.
At lower temperatures, we are especially interested in the production of molecular hydrogen, and so we follow the ionization level and H2 abundance across the shock. The effect of in-shock cooling is substantial: the maximum temperature the gas reaches compared with the theoretical temperature is found to vary between 0.15 and 0.81, depending upon the shock strength and mass resolution. The downstream ionization level is reduced from the theoretical level by a factor of between 2.4 and 12.5, and the resulting H2 abundance by a factor of 1.35 to 2.22.
At temperatures above 105 K, radiative shocks are unstable and will oscillate. We find that the shock jump temperature varies by a factor of 20 because of these oscillations.
We conclude that extreme caution must be exercised when interpreting the results of simulations of galaxy formation.  相似文献   

13.
The propagation of a spherical shock wave in an ideal gas with heat conduction and radiation heat-flux, and with or without self-gravitational effects, is investigated. The initial density of the gas is assumed to obey a power law. The heat conduction is expressed in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density, and the total energy of the wave to vary with time. Similarity solutions are obtained and the effects of variation of the heat transfer parameters, the variation of initial density and the presence of self-gravitational field are investigated.  相似文献   

14.
Abstract— We have studied the CB carbonaceous chondrites Queen Alexandra Range (QUE) 94411, Hammadah al Hamra (HH) 237, and Bencubbin with an emphasis on the petrographical and mineralogical effects of the shock processing that these meteorite assemblages have undergone. Iron‐nickel metal and chondrule silicates are the main components in these meteorites. These high‐temperature components are held together by shock melts consisting of droplets of dendritically intergrown Fe,Ni‐metal/sulfide embedded in silicate glass, which is substantially more FeO‐rich (30–40 wt%) than the chondrule silicates (FeO <5 wt%). Fine‐grained matrix material, which is a major component in most other chondrite classes, is extremely scarce in QUE 94411 and HH 237, and has not been observed in Bencubbin. This material occurs as rare, hydrated matrix lumps with major and minor element abundances roughly similar to the ferrous silicate shock melts (and CI). We infer that hydrated, fine‐grained material, compositionally similar to these matrix lumps, was originally present between the Fe,Ni‐metal grains and chondrules, but was preferentially shock melted. Other shock‐related features in QUE 94411, HH 237, and Bencubbin include an alignment and occasionally strong plastic deformation of metal and chondrule fragments. The existence of chemically zoned and metastable Fe,Ni‐metal condensates in direct contact with shock melts indicates that the shock did not substantially increase the average temperature of the rock. Because porphyritic olivine‐pyroxene chondrules are absent in QUE 94411, HH 237, and Bencubbin, it is difficult to determine the precise shock stage of these meteorites, but the shock was probably relatively light (S2–S3), consistent with a bulk temperature increase of the assemblages of less than ?300 °C. The apparently similar shock processing of Bencubbin, Weatherford, Gujba (CBa) and QUE 94411/HH 237 (CBb) supports the idea of a common asteroidal parent body for these meteorites.  相似文献   

15.
Similarity solutions for propagation of plane shock waves in a relativistic gas, where the nucleon number density varies linearly as distance from its edge at near vacuum is obtained. The shock front moves with constant speed and the solutions are applicable only to an isothermal medium or cold gas.  相似文献   

16.
Self-similar solutions for adiabatic and isothermal flows driven out by a propelling contact surface, moving into a quiet solar wind region, are investigated in the presence of magnetic field. The total energy of the flow between the shock and the contact surface is taken to be time-dependent obeying a power-law. The shock is assumed to be strong and propagating into a perfect gas at rest with non uniform density and magnetic field.  相似文献   

17.
Korteweg-de-Vries-Burger (K-dVB) equation is derived for ion acoustic shock waves in electron-positron-ion plasmas. Electrons and positrons are considered superthermal and are effectively modeled by a kappa distribution in which ions are as cold fluid. The analytical traveling wave solutions of the K-dVB equation investigated, through the (G′/G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the shock waves are derived from the traveling waves. It is observed that the amplitude ion acoustic shock waves increase as spectral index κ and kinematic viscosity η i,0 increases in which with increasing positron density β and electron temperature σ the shock amplitude decreases. Also, numerically the effect different parameters on the nonlinearity A and dispersive B terms and wave velocity V investigated.  相似文献   

18.
The kinematics of Planetary Nebulae are analyzed in terms of the solutions to the equations of hydrodynamic equilibrium developed by J. Cantó. We apply our analysis to the Planetary Nebulae NGC 6905 and NGC 6537. A detailed spectroscopic study of these objects reveals the existence of high nuclear velocities, together with complex kinematic structures and unusual emission line intensities. Shock ionization clearly plays a key role in these nebulae. Remarkably good agreement is obtained when comparing the synthetic maps and spectra resulting from the shock solutions with the observational data.  相似文献   

19.
In the present paper, we have obtained some exact analytic self-similar solutions for a zero-temperature gradient behind a magnetogasdynamic shock wave produced by stellar explosions. The initial density of the medium is taken to vary as some power of the distance from the point of explosion. The solutions are obtained for the cases when the energy of the shocked gas is constant, the energy is varying, and the shock velocity is constant. General solutions are also obtained. We have also analytically obtained the position of the singular surface behind the shock wave.  相似文献   

20.
We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy     , the specific angular momentum (λ) and the accretion rate     of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the     plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate     , the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.  相似文献   

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