Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.     

Relativistic hydrodynamics of a free expansion and a shock wave in one-dimension

Dynamical evolution of a relativistic explosion resulting from a large amount of energy release in a homogenous medium is studied using the Khalatnikov equation describing relativistic, hydrodynamic, planar flow. The early phase of the explosion is idealized to two stages: a free expansion and a shock wave stage. By the hodograph transformation inverting the dependent and independent variables, the hydrodynamic equations for the relativistic flow are reduced to second-order linear equations in a velocity-enthalpy space and they are solved by the method of Laplace transformation. The propagation laws and flow structures of the relativistic expansion are obtained at each stage. In the free expansion stage, the flow with a sufficiently high sound velocity forms a thin shell of the energy density in the comoving frame at the front and accelerates the front. In the shock wave stage, the Lorentz factor of the shock front decreases logarithmically with time. The transition time from a free expansion to a shock wave stage suggests that the super-light expansion observed in extragalactic radio sources has no spherical geometry but must be confined to a narrow cone.     

Dissipative accretion flows around a rotating black hole

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.     

Shock waves from point-sources in a heat-conducting gas

The shock wave produced by a point source has been studied in a heat-conducting gas medium. The shock is assumed to be strong enough to neglect the ambient gas pressure and the similarity method is used. The distribution of flow quantities behind the shock have been obtained by the numerical integration of a system of ordinary differential equations using the boundary conditions at the shock wave.     

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

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.     

Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics

A self-similar flow of a perfect gas behind a strong shock driven out by a propelling contact discontinuity surface moving with time according to an exponential law in the presence of axial component of the magnetic field is investigated. The flow between the shock and the inner-expanding surface is assumed to be isothermal. The infinite electrically conductive and uniform medium has been taken into consideration.     

The emergence of a spherical magnetogasdynamic shock wave at the surface of a star

The propagation of a magnetogasdynamic shock wave originating in a stellar interior, is ocnsidered when it approaches the surfaces of the star. The flow behind the shock wave is assumed isothermal rather than adiabatic to stimulate the conditions of large radiative transfer near the stellar surface. The product solution of McVittie has been used to obtain exact solution of the problem. It has been obtained that velocity, density, pressure and magnetic field increases as we move from shock surface towards the nucleus of the star.     

Self-similar flows behind a spherical radiation-driven shock wave,II

Self-similar flows, behind a radiation-driven shock wave, have been investigated in non-uniform atmosphere. The total energy content of the flow behind the shock increases due to the absorption of radiation and it is assumed to be time-dependent.     

On the boundary conditions on a shock wave for hypersonic flow around a descent vehicle

Stationary hypersonic flow around a descent vehicle is examined by considering equilibrium and nonequilibrium reactions. We study how physical-chemical processes and shock wave conditions for gas species influence the shock-layer structure. It is shown that conservation conditions of species on the shock wave cause high-temperature and concentration gradients in the shock layer when we calculate spacecraft deceleration trajectory in the atmosphere at 75 km altitude.     

Standing shocks in magnetized dissipative accretion flow around black holes

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.     

A self-similar flow of self-gravitating gas behind a shock wave with increasing energy,I

Self-similar flows of self-gravitating gas behind a spherical shock wave which are driven out by a propelling contact surface, propagating in a nonuniform atmosphere at rest, are investigated. The total energy content of the flow between a shock front and contact surface is taken to be time-dependent. In brief, the self-similar homothermal flows of self-gravitating gas behind a shock wave and Roche's model case are also studied in the present paper.     

A shock hodograph in collisionless plasma

In this paper, the shock hodograph (polar) for a collisionless transverse shock has been developed in the plane of the flow deflection angle and total pressure jump. The sonic point on the hodograph lies closer to the characteristic than to the point of maximum flow deflection for an attached shock. This hodograph is particularly useful in the analysis of three shock confluences and refraction of shock waves at gas interfaces. The first analysis is fully described in this paper. It is observed that the third shock wave is forward facing. It is pertinent to note that the limited region of supersonic flow also restricts the occurrences of three shock interactions.     

Spherical radiation-driven shock waves in a non-uniform atmosphere

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.     

Jump relations across a shock in non-ideal gas flow

Generalized forms of jump relations are obtained for one dimensional shock waves propagating in a non-ideal gas which reduce to Rankine-Hugoniot conditions for shocks in idea gas when non-idealness parameter becomes zero. The equation of state for non-ideal gas is considered as given by Landau and Lifshitz. The jump relations for pressure, density, temperature, particle velocity, and change in entropy across the shock are derived in terms of upstream Mach number. Finally, the useful forms of the shock jump relations for weak and strong shocks, respectively, are obtained in terms of the non-idealness parameter. It is observed that the shock waves may arise in flow of real fluids where upstream Mach number is less than unity.     

The termination shock in a striped pulsar wind

The origin of radio emission from plerions is considered. Recent observations suggest that radio-emitting electrons are presently accelerated rather than having been injected at early stages of the plerion evolution. The observed flat spectra without a low-frequency cut-off imply an acceleration mechanism that raises the average particle energy by orders of magnitude but leaves most of the particles at an energy of less than approximately a few hundred MeV. It is suggested that annihilation of the alternating magnetic field at the pulsar wind termination shock provides the necessary mechanism. Toroidal stripes of opposite magnetic polarity are formed in the wind emanating from an obliquely rotating pulsar magnetosphere (the striped wind). At the termination shock, the flow compresses and the magnetic field annihilates by driven reconnection. Jump conditions are obtained for the shock in a striped wind. It is shown that the post-shock magnetohydrodynamic parameters of the flow are the same as if the energy of the alternating field had already been converted into plasma energy upstream of the shock. Therefore, the available estimates of the ratio of the Poynting flux to the matter energy flux, σ, should be attributed not to the total upstream Poynting flux but only to that associated with the average magnetic field. A simple model for the particle acceleration in the shocked striped wind is presented.     

A self-similar flow behind a spherical shock wave with thermal radiation,I

Similarity solutions, for one-dimensional unsteady flow of a perfect gas behind a spherical shock wave produced on account of a sudden explosion or driven out by an expanding piston including the effects of radiative cooling, are investigated. The shock ahead of the point of explosion or piston is propagating into a transparent medium at rest with non-uniform density. The total energy of the wave is assumed to be time dependent obeying a power law.     

An exact similarity solution in radiation magneto-gas-dynamics for the flows behind a spherical shock wave

An exact similarity solution for a spherical magnetogasdynamic shock is obtained in the case when radiation energy, radiation pressure and radiative heat flux are important. The total energy of the shock wave increase with time. We have shown that due to the magnetic field the flow variables are considerably changed. Also, due to increases in radiation pressure number the radiation flux is increased.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

Shock jump relations for a dusty gas atmosphere

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows.     

A universal vertical stellar density distribution law for the Galaxy

This article applies nonstandard analysis to derive jump conditions for one-dimensional, diverging, magnetogasdynamic shock waves emerging on the surface of a star. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions for the flow parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters. It is shown here that the equations modeling a family of magnetogasdynamic shock waves yield products of generalized functions that may be analyzed consistently using nonstandard predistributions.