Post-shock Flow Research Articles

Gasdynamical Stability of Shear Flow in Spiral Arms of Disk Galaxies

Using a linear, finite difference hydrodynamic code, we investigate the dynamical stability of gas flow within the spiral arms of disk galaxies by considering an initial value problem. Assuming a shock to be present, we test the postshock stability of the flow in the presence of rapidly varying shear, which is characteristic of the region adjacent to shocks in spiral arms. Our method involves carrying out a linearized perturbation analysis on the postshock flow. The perturbations have a simple plane wave form in the azimuthal direction. We include radial as well as azimuthal velocities in the background flow. The region under investigation extends from the shock front to the location at which the radial velocity becomes supersonic. This is a semiglobal calculation in the sense that its extent is small on a galactic scale but encompasses postshock flow structure. We do not consider sell-gravity here. Despite the existence of several potentially destabilizing elements, the flows examined were found to be linearly stable, in general agreement with millimeter-wave observations of laminar flow structure in M51. In particular, the shock is Kelvin-Helmholtz stable, and the inner hard-wall boundary conditions do not lead to global Papaloizou-Pringle instabilities. The key stabilizing feature of the flow appears to be the presence of radial velocity. We suggest that radial flow stabilizes galactic shocks by altering the nature of the dynamics at the corotation radius of the semiglobal mode. Since fluid elements of the unperturbed system cannot comove with the modal pattern speed, energy exchange is profoundly affected. This may also at least partly account for why it is that accretion markedly stabilizes disks that are linearly unstable to Papaloizou-Pringle modes.

Flat-plate boundary-layer flows induced by dusty shock wave

When a dusty shock wave propagates along a flat plate, laminar boundary-layer flows are formed over the solid wall. The induced boundary layer problem is numerically investigated in the present paper. Using a two-continuum medium and twoway coupling model, the governing equations for this two-phase flow system are given and then solved by the finite difference method. The calculation results indicate that the post-shock flow field is characterized by relaxation phenomenon. The effects of the relaxation structure of the dusty shock wave on the boundary layer are discussed in detail.

Signatures of fast CMEs in interplanetary space

While fast coronal mass ejections (CMEs) have been uniquely identified as sources of transient shock-disturbances in interplanetary space, it is less understood why different kinds of plasma and magnetic field signatures are found in the individual post-shock flows. It is an open question if CMEs can produce various types of solar wind ejecta, e.g. magnetic flux ropes or flows without highly ordered internal fields. To help further clarify the consequences of fast CMEs in interplanetary space we have examined shock events measured by the Helios 1 spacecraft during the years 1979–1981 for which the associated CME has been directly observed with the coronagraph onboard the P78/1 satellite. Seventeen (68%) out of 25 shock-disturbances were followed by clearly discernible driver gas signatures, but only 7 (41%) of the driver gases were magnetic clouds.

Stable and Unstable Accretion Flows with Angular Momentum near a Point Mass

The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of thin accretion flows with vanishing thickness, we show that the governing equations become self-similar, involving no free parameters. We study numerically thin accretion flows with finite thickness as well as those with vanishing thickness. Mass elements of the incoming flow enter the computational regime as thin rings. In the case with finite thickness, after a transient period of initial adjustment, an almost steady-state accretion shock with a small oscillation amplitude forms, confirming the previous work by Molteni, Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity between the funnel wall and the accretion shock follows closed streamlines, forming a torus. This torus, in turn, behaves as an effective barrier to the incoming flow and supports the accretion shock which reflects the incoming gas away from the equatorial plane. The postshock flow, which is further accelerated by the pressure gradient behind the shock, goes through a second shock which then reflects the flow away from the symmetry axis to form a conical outgoing wind. As the thickness of the inflowing layer decreases (or if the ratio of the half thickness to the distance to the funnel wall along the equatorial plan is smaller than $\sim0.1$), the flow becomes unstable. In the case with vanishing thickness, the accretion shock formed to stop the incoming flow behind the funnel wall oscillates quasi-periodically with an amplitude comparable to the thickness. The structure between the funnel wall and the accretion shock is destroyed as the shock moves inwards toward the central mass and re-generated

The response of a gasdynamic termination shock to interplanetary disturbances

A one‐dimensional gasdynamic model is used to analyze the interaction of the solar wind termination shock (TS) with various interplanetary disturbances. These include density enhancements and depletions, Gaussian “shock” pulses, and forward‐reverse shock pairs. Our simulations suggest that the termination shock is unlikely to be stationary. Both the interaction state and the postinteraction state of the termination shock are discussed. The very complicated state and structure of the TS during interaction with interplanetary disturbances is examined carefully. It is found that the TS is not readily identifiable from the other simultaneously present structures (reverse shock, contact discontinuities, forward shocks and so on.). This may complicate the identification of the TS by the Voyager or Pioneer spacecraft significantly. It is also found that a number of interesting structures propagate and evolve downstream after a collision. These include sharp spikes in the density, which advect outward at the postshock flow speed, and secondary damped shock pulses produced in the collision, which propagate supersonically. Some implications of both the density enhancements and the production of damped shock waves in the heliosheath and at the heliopause are discussed.

Numerical study of shock diffraction in dusty gases

In the present paper, a two-fluid model with interphase coupling effects is applied to dilute gas-particle systems. In order to study the characteristics of shock diffraction around a sharp 90 degree corner in the dusty gas, we adopt the operator-splitting technique and high-resolution numerical method, reveal the changes of diffraction pattern due to particle presence, and discuss the effects of particle properties on post-shock flow field.

Nonlinear instability of accelerating shock waves with application to supernovae

We consider the stability of a planar accelerating shock front in an exponential atmosphere, a situation that can be described by a self-similar solution. A previous linear instability analysis showed that there are three regimes, depending on the wavelength of the perturbation along the direction of the shock front: at long wavelengths the shock is unstable, at intermediate wavelengths it is overstable, and at short wavelenghts it is stable, where the characteristic length is set by the initial density scale height. We have carried out numerical simulations of such an accelerating shock front and have confirmed the results of the semianalytic linear analysis in the linear regime. In the nonlinear regime, the evolution again depends on the three wavelength domains. At long wavelengths, the instability continuously grows but the flow remains smooth, and at short wavelengths, the flow is stable. The intermediate wavelength, overstable regime shows more complex evolution. The growing linear oscillations saturate soon after entering the nonlinear regime and the oscillations continue with the same approximate period. The shock front develops moving points of intersection, which generate weak shock fronts and density and pressure structure in the immediate postshock flow. The density fluctuations, with a contrast of a factor of 2-3, become frozen into the downstream flow. The growth of the instability is slow, so substantial initial perturbations are needed; thesemay be present in Type II supernovae with red supergiant progenitor stars which have outer convective regions. The clumping in the outer supernova atmosphere may affect spectral line formation and may play a role in the formation of fast knots.

A study of X-ray and infrared emissions from dusty nonradiative shock waves

We have constructed models that predict the dynamic evolution and infrared (IR) emission of grains behind nonradiative shock waves. We present a self-consistent treatment of the effect of grain destruction and heating on the ionization structure and X-ray emission of the postshock gas. Incorporating thermal sputtering, collisional heating, and deceleration of grains in the postshock flow, we predict the IR and X-ray fluxes from the dusty plasma as a function of swept-up column density. Heavy elements such as C, O, Mg, S, Si and Fe are initially depleted from the gas phase but are gradually returned as the grains are destroyed. The injected neutral atoms require some time to 'catch up' with the ionization state of the ambient gas. The nonequilibrium ionization state and gradient in elemental abundances in the postshock flow produces characteristic X-ray signatures that can be related to the age of the shock and amount of grain destruction. We study the effects of preshock density and shock velocity on the X-ray and IR emission from the shock. We show that the effects of graindestruction on the X-ray spectra of shock waves are substantial. In particular, temperatures derived from X-ray spectra of middle-aged remnants are likely to be overestimated by approximately 15% if cosmic abundances are assumed. Due to the long timescales for grain destruction in X-ray gases over a wide range of temperatures, we suggest that future X-ray spectra studies of supernova remnants be based on depleted abundances instead of cosmic abundances. Our model predictions agree reasonably well with IRAS and Einstein IPC observations of the Cygnus Loop.

The origin of forbidden line emission from young stellar objects

We present a model for the origin of blueshifted, optical forbidden line emission and jets in young stellar objects based on generic properties of hydromagnetic disk winds. Magnetic stresses recollimate hydromagnetic disk winds to magnetic focal regions under very general conditions. We demonstrate that conditions in MHD shocks at these points account for the observed emission. We find that for fiducial accretion rates of 10(-7) M. yr-1 and magnetic fields at the inner edge of the disk (congruent-to 10(12) cm, gas accelerated from the innermost parts of a Keplerian accretion disk focuses into regions greater-than-or-equal-to 0.4 AU in radius that lie congruent-to 16 AU above and below the disk. The shocked gas density ranges from congruent-to 10(4) to 10(8) cm-3 where the latter occurs in the innermost part of the flow and shock. Shocked gas speeds range up to 250 km s-1 (going from the outer part of the shock at congruent-to 2 AU, to the innermost region) under these conditions. The magnetic field is moderately amplified in the shock and diverges from the flow axis in the postshock flow. It is this feature of MHD shock that produces an expanding cone of shocked gas. The opening angle of the postshock gas with respect to the flow axis is 40-degrees, and this accounts for the double-peaked character of the line profiles. Our model also predicts that the slower velocity component is associated with shocked gas of lower density than that associated with the higher velocity component. We show that the wind is largely neutral with an electron fraction of 10(-1). The wind remains largely neutral in adiabatic MHD shocks because much of the preshock kinetic energy goes into an increased postshock magnetic field. Substantial fractions of the flow energy can be liberated in these shocks.

Imprints of the interstellar medium on location, geometry and nature of the heliospheric shock

The fact of a relative motion of the solar system with respect to the ambient interstellar medium causes a series of qualitatively very different physical influences on both the supersonic and the subsonic solar wind plasma regimes. We are quantifying some of these influences here which are connected with the action of interstellar neutral gas atoms, low and high energy plasmas and magnetic fields. As is shown quantitatively here the distribution of neutral interstellar gases in the heliosphere, and the interplanetary UV/EUV glows and pick-up ion fluxes connected with it, have received clear imprints from the ionized component of the interstellar medium which, when carefully analysed, will permit the derivation of many unknown parameters of this component. From our synoptic analysis of distant upwind and downwind interplanetary Lyman-Alpha data we shall conclude that these data can only be reconciled under the strong plead for a termination shock at an upwind distance of about 50 to 70 AU. No clearcut answer, however, can be given as to why the shock is forced to be located such close to the sun. Furthermore we derive theoretical arguments why the heliospheric shock and the supersonic solar wind approaching it should have pronounced upaxis/downaxis asymmetries which when clearly determined could reveal a tilt of this axis with respect to the neutral interstellar wind vector and thereby give some clear hints towards the magnitude and the direction of the interstellar magnetic field. Starting from theoretical solutions for the postshock plasma flows which are consistent with the flow of the ambient interstellar medium we derive the location and geometry of the solar termination shock converting an inner supersonic solar wind to this postshock flow.

The stability of cosmic-ray-dominated shocks - A secondary instability

Previous studies in one spatial dimension showed that the precursors of cosmic-ray-dominated shocks are unstable against traveling acoustic disturbances. Here we report that a secondary, Rayleigh-Taylor type instability can exist in cosmic-ray-dominated media influenced by the acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the one-dimensional acoustic instability itself in the cases we have considered. The nonlinear development has been followed numerically with a two-dimensional PPM hydrodynamics code that also incorporates the two-fluid cosmic-ray energy equation. We show that the secondary instability may cause the precursor and postshock flows to become highly turbulent.

Hydrodynamic instability of accretion flows and wind flows with standing shock waves

The hydrodynamic instability of isothermal, inviscid and axisymmetric accretion (and wind) flows with standing shock waves is studied against infinitesimal, isothermal and axisymmetric perturbations. The post-shock flow is assumed to be transonic so that accretion on to black holes can be treated. A global stability analysis shows that the value of an unperturbed quantity, ν≡−(1/V) (dΦ eff /dr−c s 2 /r) at the post-shock side of the unperturbed shock location determines stability properties, where V, c s and Φ eff are, respectively, the radial flow velocity, the isothermal sound speed, and effective gravitational potential including the centrifugal force

Structure of wiggly-cosmic-string wakes.

We investigate the structure of wiggly-cosmic-string wakes by solving the fluid equations of motion under some simplifying assumptions. The flow of collisionless matter is treated first. Then the flow of a non-self-gravitating, nonrelativistic, ideal fluid is studied and the density structure of the wake is found. For typical values of the string tension, strong shocks are formed in the wakes after the epoch of recombination. It is shown that the post-shock fluid flow in these wakes will be vortical and the vorticity will lead to the generation of a magnetic field. A potential problem in the cosmic-string scenario for structure formation and its possible resolutions are discussed.

The semiannual variation of great geomagnetic storms and the postshock Russell‐McPherron effect preceding coronal mass ejecta

The occurrence rate of great geomagnetic storms displays a pronounced semiannual variation. Of the forty‐two great storms during the period 1940–1990, none occurred during the solstitial months of June and December, and 40% (17) occurred during the equinoctial months of March and September. This suggests that the semiannual variation found by averaging indices is not the result of some statistical effect superposed on the effects of random storm occurrence but rather is dominated by the storms themselves. Recent results indicate that the intense southward interplanetary magnetic fields (IMFs) responsible for great storms can reside in the postshock plasma preceding the driver gas of coronal mass ejections (CMEs) as well as in the driver gas itself. Here we propose that strong southward fields in the postshock flow result from a major increase in the Russell‐McPherron polarity effect through a systematic pattern of compression and draping within the ecliptic plane. Differential compression at the shock increases the Parker spiral angle and, consequently, the azimuthal field component that projects as a southward component onto Earth's dipole axis. The resulting prediction is that southward fields in the postshock plasma maximize at the spring (fall) equinox in CMEs emerging from toward (away) sectors. This pattern produces a strong semiannual variation in postshock IMF orientation and may account at least in part for the observed semiannual variation of the occurrence of great geomagnetic storms.

Radiative shocks and hydrogen molecules in pregalactic gas - The effects of postshock radiation

Previous calculations of radiative shocks in pregalactic gas are generalized and substantially improved. The hydrodynamical conservations are solved, along with the rate equations for nonequilibrium ionization, recombination, and molecule formation, and the equation of radiative transfer, for steady-state shocks in a gas of primordial compositions. This calculation self-consistently includes the effects of the diffuse postshock emission as well as a possible external radiation flux on the postshock flow and the preshock ionization levels. A previous result is confirmed that the shocked gas cools faster than it can recombine and, as a result, is able to form an H2 concentration as high as 0.003 via the formation of H(-) and H2(+) intermediaries due to the enhanced nonequilibrium ionization fraction at 10,000 K. It is shown that, as the level of the external radiation flux is increased, the formation of and cooling by H2 molecules can be inhibited and delayed. The detailed radiation spectra and ionizing photon number fluxes emergent from these shocks are presented.

Colliding winds from early-type stars in binary systems

The dynamics of the wind and shock structure formed by the wind collision in early-type binary systems is examined by means of a 2D hydrodynamics code, which self-consistently accounts for radiative cooling, and represents a significant improvement over previous attempts to model these systems. The X-ray luminosity and spectra of the shock-heated region, accounting for wind attenuation and the influence of different abundances on the resultant level and spectra of X-ray emission are calculated. A variety of dynamical instabilities that are found to dominate the intershock region is examined. These instabilities are found to be particularly important when postshock material is able to cool. These instabilities disrupt the postshock flow and add a time variability of order 10 percent to the X-ray luminosity. The X-ray spectrum of these systems is found to vary with the nuclear abundances of winds. These theoretical models are used to study several massive binary systems, in particular V444 Cyg and HD 193793.

The stability of an accelerating shock wave in an exponential atmosphere

The stability of a self-similar solution for an accelerating shock wave in an exponential atmosphere is studied using a linearized, normal mode analysis. An eigenvalue is determined by passing the solution through a critical point in the postshock flow. While instability is present over a wide range of parameters, the growth rate of the instability is slow. The shock front must travel four scale heights for a doubling in magnitude of a linear perturbation under the most favorable conditions for growth. The instability is expected to operate in a similar way for other accelerating shock fronts in steep density gradients. Substantial initial peturbations are needed for significant effects; this may occur in type Ia SNe and in the SN giving rise to Cas A. 27 refs.

Turbulent collisional ionising shock waves in argon

Using an arc-driven shock tube, the turbulent features in the ion density fluctuations of an argon plasma behind collisional ionising shock fronts are determined. Fluctuation power spectra show many discrete modes and follow S(Kz) alpha Kz-n with 1.2<n<2.2 for shock wave Mach numbers between 15 and 71. The overall turbulent properties are found to be almost frozen with the post-shock flow and to have particle-like dynamical behaviour.

Parametric analysis on the post-shock wave relaxation zone of carbon particle-laden oxygen gas

The dependence of the postshock flow field in two-phase detonation on the initial carbon mass loading and the initial carbon particle diameter has been examined in this study, and it was found that their effects were noticeable in the thermal and fluid mechanical properties as well as the total relaxation zone length. The relaxation zone length was observed to decrease either as the carbon mass loading increased or as the initial carbon particle diameter decreased. Depending on the initial loading ratio, the suspension properties reached a disparate final equilibrium state. However, changing the initial carbon particle diameter for a given carbon mass loading did not affect the postshock equilibrium state.

Dusty Shock Waves

The flow field developed behind shock waves in a pure gaseous medium is well known and documented in all gasdynamics textbooks. This is not the case when the gaseous medium is seeded with small solid particles. The present review treats various cases of shock waves propagation into a gas-dust suspension (dusty shock waves). It starts (chapter 1) with basic definitions of two-phase (gas-dust) suspensions and presents a general form of the conservation equations which govern dusty shock wave flows. In chapter two, the simple case of a steady flow of a suspension consisting of an inert dust and a perfect gas through a normal shock wave is studied. The effect of the dust presence, and of changes in its physical parameters, on the post-shock wave flow are discussed. Obviously, these discussions are limited to relatively weak shock waves (perfect gas). For stronger normal shock waves, the assumption of a perfect gas no longer holds. Therefore, in chapter three, real gas effects (ionization or dissociation) are taken into account when calculating the post-shock flow field. In chapter four, the dust chemistry is included and its effects on the post-shock flow is studied. In order to emphasize the role played by the dust chemistry, a comparison between a reactive and a similar inert suspension is presented. The case of an oblique shock wave in a dusty gas is discussed in chapter five. In all cases treated in chapters two to five the flow is steady; however, in many engineering applications this is not the case. In reality, even for the simplest case of a one-dimensional flow (normal shock wave propagation into quiescent suspension—the dusty shock tube) the shock wave attenuates and the flow field behind it is not steady. This case is treated in chapter six. The cases treated in chapters two to six deal with planar shock waves. However, all explosion generated shock waves in the atmosphere are spherical. Due to the engineering importance of this case, the post-shock flow for spherical shock waves in a dusty gas is studied, in detail, in chapter seven. It is shown in the present review that the dust presence has significant effects on the post-shock flow field. In all cases studied, a relaxation zone is developed behind the shock wave front. Throughout this zone momentum and energy exchange between the two phases of the suspension takes place. Through these interactions a new state of equilibrium is reached. The extent of the relaxation zone depends upon the dust loading ratio, the dust particle diameter, its specific heat capacity, and the dust spatial density. Due to the complexity of conducting experimental investigations with dusty shock waves, the number of published experimental results is very limited. As a result most of the present review contains numerical studies. However, in the few cases where experimental data are available, (e.g. dusty shock tube flow; see chapter six) a comparison between the numerical and experimental results is given.