Effects of Initial Conditions on Compressible Mixing in Supernova-Relevant Laboratory Experiments

In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen–helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. This paper represents a summary of recent results from a computational study of unstable systems driven by high Mach number shock and blast waves. For planar multimode systems, compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (ICs) by allowing for memory of the initial conditions to be retained in the mix-width at all times. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. Initial conditions predicted by some recent stellar calculations are incompatible with self-similarity.     

Shock waves and vorticity generation in protogalactic medium

A theory of secondary vorticity is suggested on grounds of an isotropic Hot Big Bang. Vortical motions are generated in front of the shock waves, which appear as a result of supersonic hydrodynamic processes induced by gravitational instability at a later epoch of cosmological expansion. Inside large layers of gas compressed by shocks subsonic turbulence with both vortical and acoustic modes develops. Every such layer may be treated as a protocluster; and eddies, if strong enough, would give rise to protogalaxies. An effective mechanism of vorticity generation — scattering of density inhomogeneities on shock fronts — is examined in detail. Quantitative estimates show that the vortices that are due to this mechanism can be at least the order of magnitude to account for the angular mometa of spiral galaxies. The spectrum of initial irrotational perturbations remains open to discussion, but characteristic amplitudes required do not contradict any observational or theoretical restrictions.     

Preheat Issues in Hydrodynamic Hedla Experiments

Hydrodynamic experiments have become a very active area within High Energy Density Laboratory Astrophysics. In such experiments, preheat of an interior surface due to heating prior to shock arrival can alter the initial conditions for further evolution and can change the nature of the experiment (Olson et al., 2003). Unfortunately, preheat cannot typically be detected without undertaking dedicated experiments for this purpose. We have designed such experiments, relevant to hydrodynamic instability experiments using Omega Laser at intensities of ~10¹⁵ W/cm². Simulations using the HYADES code suggest that radiative preheat alone causes the interface to move approximately 2 μm before the blast wave reaches it. Hot-electron preheat could cause much larger motions. These experiments will use VISAR to examine the motion of an aluminum sample layer at the rear interface of a standard hydrodynamic target during the period before the shock reaches it (Allen and Burton, 1993).     

The effect of Alfvén waves on MHD fast shocks

The Rankine-Hugoniot equations for hydromagnetic shocks are extended to include the energy and momentum flux due to Alfvén waves incident on the shock. The shock relations are solved numerically for a wide variety of parameters typical of interplanetary conditions. The presence of the waves can cause appreciable changes in the structure of fast shocks of low Mach number.     

Small-Amplitude Disturbances in a Radiating and Scattering Grey MediumIII. Gravitational Effects on the Solutions of Given Real Wave Number k

We study the fundamental modes of radiation hydrodynamic linear waves that arise from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium by taking into account the gravitational effects. The equation of radiative acoustics is derived from three hydrodynamic equations, Poisson’s equation, and two moment equations of radiation, by assuming a spherical symmetry for the matter and radiation and by using the Eddington approximation. We solve the dispersion relation as a quintic function of angular frequency ω, the wave number k being a real parameter. Numerical results reveal that wave patterns of five solutions are distinguished into three types: the radiation-dominated, type 1, and type 2 matter-dominated cases. In the case of no gravitaional effects (Kaneko et al., 2005), the following wave modes appear: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusions, adiabatic sound wave, cooling-damped and drag-force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. Meanwhile, the gravitaional effects being taken into account, the growing gravo-diffusion mode newly arises from the constant-pressure diffusion at the point that k agrees with Jeans’ wave number specified by the isothermal sound speed. This mode changes to the growing radiation-acoustic gravity mode near the point that k becomes Jeans’ wave number specified by the isentropic radiation-acoustic speed. In step with a transition between them, the isentropic radiation-acoustic wave splits into the damping radiation-acoustic gravity mode and constant-volume diffusion. The constant-volume diffusion emerges twice if the gravitational effects are taken into account. Since analytic solutions are derived for all wave modes, we discuss their physical significance. The critical conditions are given which distinguish between radiation-dominated and type 1 matter-dominated cases, and between type 1 and type 2 matter-dominated cases. Waves in a self-gravitating scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.     

The Seismic Efficiency of Space Body Impacts

The numerical analysis of the propagation of shock waves initiated by either a space body striking the Earth’s surface, or underground explosions, allows us to compare the energies required to attain the same amplitudes of shock waves at impacts and explosions. Proceeding from this and based on the data of seismic efficiency of underground explosions, the authors have estimated the fraction of the kinetic energy of a space body transformed into the energy of seismic disturbances when the body strikes the Earth. This fraction is about 10^–3, which is an order of magnitude more than the most common estimates. Space bodies decelerating and collapsing in the atmosphere also generate seismic waves in the ground due to the impact of the air-shock wave on the Earth’s surface. In this case, the seismic efficiency is considerably lower, according to the calculations, it is about 10^–5.     

Cross-scale coupling at a perpendicular collisionless shock

A full particle simulation study is carried out on a perpendicular collisionless shock with a relatively low Alfven Mach number (M_A = 5). Recent self-consistent hybrid and full particle simulations have demonstrated ion kinetics are essential for the non-stationarity of perpendicular collisionless shocks, which means that physical processes due to ion kinetics modify the shock jump condition for fluid plasmas. This is a cross-scale coupling between fluid dynamics and ion kinetics. On the other hand, it is not easy to study cross-scale coupling of electron kinetics with ion kinetics or fluid dynamics, because it is a heavy task to conduct large-scale full particle simulations of collisionless shocks. In the present study, we have performed a two-dimensional (2D) electromagnetic full particle simulation with a “shock-rest-frame model”. The simulation domain is taken to be larger than the ion inertial length in order to include full kinetics of both electrons and ions. The present simulation result has confirmed the transition of shock structures from the cyclic self-reformation to the quasi-stationary shock front. During the transition, electrons and ions are thermalized in the direction parallel to the shock magnetic field. Ions are thermalized by low-frequency electromagnetic waves (or rippled structures) excited by strong ion temperature anisotropy at the shock foot, while electrons are thermalized by high-frequency electromagnetic waves (or whistler mode waves) excited by electron temperature anisotropy at the shock overshoot. Ion acoustic waves are also excited at the shock overshoot where the electron parallel temperature becomes higher than the ion parallel temperature. We expect that ion acoustic waves are responsible for parallel diffusion of both electrons and ions, and that a cross-scale coupling between an ion-scale mesoscopic instability and an electron-scale microscopic instability is important for structures and dynamics of a collisionless perpendicular shock.     

Traveling waves in the martian atmosphere from MGS TES Nadir data

We have characterized the annual behavior of martian atmospheric traveling waves in the MGS TES data set from the first two martian years of mapping. There is a high degree of repeatability between the two years. They are dominated by strong low zonal wavenumber waves with high amplitudes near the polar jets, strongest in late northern fall and early northern winter. The m=1 waves have amplitudes up to about 20 K, are vertically extended, and occasionally extend even into the tropics. Periods for m=1 range from 2.5 to 30 sols. Much weaker waves were identified in the south, with amplitudes less than about 3.5 K. Traveling waves with m=2 and m=3 are also seen, but their amplitudes are typically limited to less than 4 K, and are generally more confined near the surface. In the north, they are more evident in fall and spring rather than winter solstice, which is clearly dominated by m=1 waves. Some evidence of storm tracks has been identified in the data, with accentuated weather-related temperature perturbations near longitudes 200° to 320° E for both the southern and northern hemispheres near latitude ±65° at the surface. Some evidence was also found for a sharpening of longitudinal gradients into what may be frontal systems. EP flux divergences show the waves extracting energy from the zonal mean winds. When the m=1 waves were strongest, decelerations of the zonal jet of order 30 m/(s sol) were measured. Above 1 scale height, the waves extract energy from the jet predominately through barotropic processes, but their character is overall mixed barotropic/baroclinic. Inertial instabilities may exist at altitude on the equatorward flanks of the polar jets, and marginal stability extends through to the tropics. This may explain the coordination of the tropical behavior of the waves with that centered along the polar jet, consistent with the ideas expressed in Wilson et al. (2002, Geophys. Res. Lett. 29, #1684) and similar to those in Barnes et al. (1993, J. Geophys. Res. 98, 3125-3148). Throughout the year, there exist large regions with the meridional gradient of PV less than zero, but they are strongest near winter solstice. Poleward of the winter jet, the regions of instability reach the surface, equatorward they do not. These regions, satisfying a necessary criterion for instability, likely explain the genesis of the waves, and perhaps also their bimodal character between surface (faster waves) and altitude (slow m=1 waves).     

On the interaction of internal gravity waves with a magnetic field – I. Artificial wave forcing

We present results from numerical simulations of the interaction of internal gravity waves (IGW) with a magnetic field. In accordance with the dispersion relation governing IGW in the presence of magnetism and rotation, when the IGW frequency is approximately that of the Alfvén frequency, strong reflection of the wave occurs. Such strong reflection markedly changes the angular momentum transport properties of the waves. In these simple models a strong, time-independent shear layer develops, in contrast to the oscillating shear layer that develops in the purely hydrodynamic case.     

Stellar wind models with Alfvén waves

It is known that stellar winds from late type stars are of mixed thermal and magnetic origin. The stellar wind model presented in this work uses the hydrodynamic equations of mass and momentum conservation and closes the system of equations with a detailed energy equation. Both momentum and energy equations have terms due to the effects of Alfvén waves. A smooth transition between the two regimes for Alfvén wave propagation, the undamped and the damped modes, is achieved by considering the geometrical mean of both wave amplitudes. It will be shown that the initial push on the plasma is provided by the mechanical heating input, and that further out the Alfvén waves take over energetically.     

On the Rayleigh–Taylor instability of radio bubbles in galaxy clusters

We consider the Rayleigh–Taylor instability in the early evolution of the rarefied radio bubbles (cavities) observed in many cooling-flow clusters of galaxies. The top of a bubble becomes prone to the Rayleigh–Taylor instability as the bubble rises through the intracluster medium (ICM). We show that while the jet is powering the inflation, the deceleration of the bubble–ICM interface is able to reverse the Rayleigh–Taylor instability criterion. In addition, the inflation introduces a drag effect which increases substantially the instability growth time. The combined action of these two effects considerably delays the onset of the instability. Later on, when the magnitude of the deceleration drops or the jet fades, the Rayleigh–Taylor and the Kelvin–Helmholtz instabilities set in and eventually disrupt the bubble. We conclude that the initial deceleration and drag, albeit unable to prevent the disruption of a bubble, may significantly lengthen its lifetime, removing the need to invoke stabilizing magnetic fields.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The propagation of nonlinear slow sausage small-amplitude waves in a magnetic slab in a magnetic environment is considered. The equation for surface waves that is allied form of the Benjamin-Ono equation and the equation for body waves that is allied form of the equation for body waves in the slab are derived with the use of the method of stretching variables. The solutions of the equation for surface waves in the form of solitary waves are obtained numerically.     

The effects of the tidal force on shear instabilities in the dust layer of the solar nebula

The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if dust/gas surface density ratio is hundreds times as large as that for the solar abundance.     

Oscillations of magnetohydrodynamic shock waves on the surfaces of T Tauri stars

This work treats the matter deceleration in a magnetohydrodynamic radiative shock wave at the surface of a star. The problem is relevant to classical T Tauri stars where infalling matter is channelled along the star's magnetic field and stopped in the dense layers of photosphere. A significant new aspect of this work is that the magnetic field has an arbitrary angle with respect to the normal to the star's surface. We consider the limit where the magnetic field at the surface of the star is not very strong in the sense that the inflow is super-Alfvénic. In this limit, the initial deceleration and heating of plasma (at the entrance to the cooling zone) occurs in a fast magnetohydrodynamic shock wave. To calculate the intensity of radiative losses we use 'real' and 'power-law' radiative functions. We determine the stability/instability of the radiative shock wave as a function of parameters of the incoming flow: velocity, strength of the magnetic field, and its inclination to the surface of the star. In a number of simulation runs with the 'real' radiative function, we find a simple criterion for stability of the radiative shock wave. For a wide range of parameters, the periods of oscillation of the shock wave are of the order of  0.02–0.2 s  .     

On the stability of galactic shocks

The stability of galactic spiral shocks is considered. A steady-state shock should be checked to see (i) if it is evolutionary; (ii) if its front is stable against bending and torsion; and (iii) if the gas flow far from the front is stable. In the present paper the evolutionary criterion is obtained, which implies that conditions in galaxies may lead to the evolutionary spiral shocks as well as to the nonevolutionary ones. In the latter case a galactic shock cannot persist — it instantly decays, emitting spontaneously spiral waves. This leads to a plausible stratification of the spiral arms, to the formation of the secondary arms, ‘spurs’ and other secondary features. The steady-state gas flow with a galactic shock (Roberts, 1969) turns out to be unstable far from the shock front, the increment being proportional to the velocity gradient. For the spiral shock calculated by Roberts (1969) the instability develops ahead of the shock front with the same growth-time of about 3×10⁷ years for all disturbance scales. This may provide a mechanism to generate turbulence of interstellar gas and to form the patchy structure of spiral arms which are known to include the structural units (gas clouds) on all possible scales.     

The weak shock in the core of the Perseus cluster

The dissipation of energy from sound waves and weak shocks is one of the most promising mechanisms for coupling active galactic nucleus (AGN) activity to the surrounding intracluster medium, and so offsetting cooling in cluster cores. We present a detailed analysis of the weak shock found in deep Chandra observations of the Perseus cluster core. A comparison of the spectra either side of the shock front shows that they are very similar. By performing a deprojection analysis of a sector containing the shock, we produce temperature and density profiles across the shock front. These show no evidence for a temperature jump coincident with the density jump. To understand this result, we model the shock formation using 1D hydrodynamic simulations including models with thermal conduction and  γ < 5/3  gas. These models do not agree well with the data, suggesting that further physics is needed to explain the shock structure. We suggest that an interaction between the shock and the Hα filaments could have a significant effect on cooling the post-shock gas.
We also calculate the thermal energy liberated by the weak shock. The total energy in the shocked region is about 3.5 times the work needed to inflate the bubbles adiabatically, and the power of the shock is around  6 × 10⁴⁴ erg s⁻¹  per bubble, just over  10⁴⁵ erg s⁻¹  in total.     

Ion-acoustic shock waves in a plasma with weakly relativistic warm ions, thermal positrons and a background electron nonextensivity

A weakly nonlinear analysis is carried out to derive a Korteweg–de Vries-Burgers-like equation for small, but finite amplitude, ion-acoustic waves in a dissipative plasma consisting of weakly relativistic ions, thermal positrons and nonextensive electrons. The travelling wave solution has been acquired by employing the tangent hyperbolic method. Our results show that in a such plasma, ion-acoustic shock waves, the strength and steepness of which are significantly modified by relativistic, nonextensive and dissipative effects, may exist. Interestingly, we found that because of ion kinematic viscosity, an initial solitonic profile develops into a shock wave. This later evolves towards a monotonic profile (dissipation-dominant case) as the electrons deviate from their Maxwellian equilibrium. Our investigation may help to understand the dissipative structures that may occur in high-energy astrophysical plasmas.     

An Operable Solution Approach to Interplanetary Hydrodynamic Shock Waves

In this paper, an operable solution approach is proposed to solve interplanetary hydrodynamic shock waves propagating in the interplanetary medium of solar wind background derived from Parker's hydrodynamic model. In our case the problem concerned is reduced to a set of ordinary differential equations (ODEs) involving the solar wind background parameters velocity v0(r), density 0(r), and pressure p0(r). The entire information for the shock can be obtained easily by obtaining the numerical solutions to the set of ODEs.     

Wave-wave interactions and gravitational instability

The instability of gravitational waves withk>k _Jeans in a weakly turbulent gas is discussed. Basic features of the processes leading to amplification or damping of gravitational waves are described. Growth rates of the amplitudes are calculated.     

Isothermal shock waves in uniform atmospheres

Similarity solutions describing the isothermal flow of a perfect gas behind shock waves are investigated for spherical symmetry. The flow is caused by a propelling contact surface (or expanding piston) and its total energy increases as a power of the time. The shock is propagating in a medium at rest with a uniform density.