Structure Of Shock Front Research Articles

Features of propagation in the atmosphere of nonlinear acoustic disturbances from pulse sources

The features of the propagation of nonlinear pulsed acoustic disturbances in the atmosphere are considered. Data are presented on the experimental observation of the formation of a shock front and the transition of a shock wave into a low-intensity acoustic wave with transformation of the pulse shape and expansion of the front at distances of more than 1000 km under conditions of both spherical and cylindrical propagation. The influence of Kelvin-Helmholtz instability during rapid gas compression on the formation of the shock front structure is discussed. Under atmospheric conditions, such instability significantly affects dissipative processes in the air and forms the front of a nonlinear wave.

МГД-волны в области предфронта межпланетных ударных волн 6 и 7 сентября 2017 г.

We analyze strong space weather disturbances during first ten days of September 2017, using the geomagnetic Dst index, parameters of normals to interplanetary shock fronts, direct measurements of interplanetary magnetic field, solar wind, and cosmic ray parameters. By applying spectral analysis methods to interplanetary medium data, we analyze MHD waves at the pre-front of two interplanetary shocks responsible for geomagnetic disturbances on September 6 and 7, 2017. The main results are as follows: the contribution of three branches of MHD waves (Alfvén, fast and slow magnetosonic) to the observed spectrum of the interplanetary magnetic field modulus has been established. We have confirmed the conclusion that the generation of Alfvén waves and fast magnetosonic waves is due to the presence of low-energy proton fluxes (Ep~1 MeV) at the pre-front of interplanetary shocks. We have also discovered a predominant contribution of slow magnetosonic waves to the observed spectrum of the interplanetary magnetic field modulus, but its reason is yet unknown. It is noted that different orientations of the normals to the interplanetary shock fronts and to the direction of the interplanetary magnetic field average vector on spacecraft located fairly close to each other may indicate waviness of the shock front structure.

MHD waves at the pre-front of interplanetary shocks on September 6 and 7, 2017

We analyze strong space weather disturbances during first ten days of September 2017, using the geomagnetic Dst index, parameters of normals to interplanetary shock fronts, direct measurements of interplanetary magnetic field, solar wind, and cosmic ray parameters. By applying spectral analysis methods to interplanetary medium data, we analyze MHD waves at the pre-front of two interplanetary shocks responsible for geomagnetic disturbances on September 6 and 7, 2017. The main results are as follows: the contribution of three branches of MHD waves (Alfvén, fast and slow magnetosonic) to the observed spectrum of the interplanetary magnetic field modulus has been established. We have confirmed the conclusion that the generation of Alfvén waves and fast magnetosonic waves is due to the presence of low-energy proton fluxes (Ep~1 MeV) at the pre-front of interplanetary shocks. We have also discovered a predominant contribution of slow magnetosonic waves to the observed spectrum of the interplanetary magnetic field modulus, but its reason is yet unknown. It is noted that different orientations of the normals to the interplanetary shock fronts and to the direction of the interplanetary magnetic field average vector on spacecraft located fairly close to each other may indicate waviness of the shock front structure.

The effects of viscosity on the structure of shock waves in a van der Waals gas

Abstract The structure of viscous shock-front has been investigated in a van der Waals gas between the boundary conditions for x = −ε and x = +ε considering the flow of a gas to be viscous and one-dimensional. The exact solutions for the flow parameters, fluid velocity, pressure, temperature, and change-in-entropy in the shock transition region have been found in view of the equation of state for van der Waals gases. The effects due to the coefficient of viscosity, shock strength, and nonidealness parameter have been analyzed on the structure and flow variable in the shock transition region. The results confirm that the thickness of shock-front increases with increasing value of the coefficient of viscosity and decreases with increasing value of the shock strength and nonidealness parameter of the gases.

Structure of a Quasi-parallel Shock Front

The aim of this study is to compare observations of the magnetic field structure of observed quasi-parallel collisionless shock fronts with the results obtained analytically. A two-fluid analytic model of the shock front structure was derived under the assumptions that the shock is stationary and planar. The ion and electron kinetic pressures were assumed to be scalar, and polytropic state equations were used. The results of this analytical approach show that the shock magnetic field has an oscillatory structure. Venus Express (VEX) observations of the Venusian bow shock have been used to validate these theoretical findings. The Venusian bow shock and corresponding foreshock are significantly smaller than those of Earth. Thus, observations of the underlying structure of the quasi-parallel shock at Venus are not masked by the presence of high-amplitude waves and nonlinear structures originating in the foreshock. It is shown that the structure of the shock front, as observed by VEX, has a very strong similarity to the structure obtained analytically.

Persistence of the steady planar normal shock structure in 3‐D unsteady potential flows

AbstractThis paper concerns the dynamic stability of the steady three‐dimensional (3‐D) wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free boundary problem of a quasi‐linear hyperbolic equation of second order in a dihedral‐space domain between the shock front and the solid wall. The key difficulty is brought by the edge singularity of the space domain, the intersection curve between the shock front and the solid wall. Different from the two‐dimensional (2‐D) case, for which the singular part of the boundary is only a point, it is a curve for the 3‐D case in this paper. This difference brings new difficulties to the mathematical analysis of the stability problem. A modified partial hodograph transformation is introduced such that the extension technique developed for the 2‐D case can be employed to establish the well‐posed theory for the initial‐boundary value problem of the linearized hyperbolic equation of second order in a dihedral‐space domain. Moreover, the extension technique is improved in this paper such that loss of regularity in the a priori estimates on the shock front does not occur. Thus, the classical nonlinear iteration scheme can be constructed to prove the existence of the solution to the stability problem, which shows the dynamic stability of the steady planar normal shock without applying the Nash–Moser iteration method.

On the Structure of a Viscous Shock-Front in a Two-Phase Gas–Particle Medium

On the Structure of a Viscous Shock-Front in a Two-Phase Gas–Particle Medium

On the structure of shock-front in a viscous and heat conducting fluids

The internal structure of one-dimensional steady shock-front is investigated using the Navier-Stokes equations in a viscous and heat conducting gaseous medium. The analytical expression and calculations for the different flow variables i.e., the particle velocity, temperature, pressure, and change-in-entropy distribution have been derived using the method of wave-front analysis. The abrupt changes in the flow variables have been observed within the shock transition region. The thickness and inverse shock-front thickness are calculated and obtained results are compared with the reported literatures. The effects on the shock structure due to the variation of different flow parameters have been discussed in each case for all the flow variables. Obtained outcomes manifests that the flow parameters i.e., coefficient of viscosity, Mach number, adiabatic index and Prandtl number exert dominant impact on the structure of shock-front, prominently.

On shockwave propagation and attenuation in poly(ethylene glycol) diacrylate hydrogels

An analytical model is developed to predict shockwave propagation and attenuation in hydrogels by combining the classical method of shock characteristics and a solution for the shock front structure. To guide the development of the model, molecular dynamics (MD) simulations are performed. Specifically, a one-dimensional shock pulse in poly(ethylene glycol) diacrylate (PEGDA) hydrogels is simulated with the nonequilibrium MD method. The role of polymer concentration on the shock response is evaluated by constructing hydrogels with 20, 35, and 50wt% PEGDA concentrations in an idealized crosslinked network. Steady-state pressure-density and shock-particle velocity relationships are established using the Murnaghan equation of state. Shock front structure is characterized by a power-law equation that relates the shock front thickness with shock pressure. These results are used as critical input for the shock propagation and attenuation model. The model is then evaluated via comparison with the classical method of characteristics. It shows significant improvement in accuracy and successfully captures salient features of shockwave attenuation, including the shock pressure amplitude, the velocities of the shock and release waves, and the attenuation timeline. Hydrogels with higher polymer concentrations exhibit a shorter attenuation time at all particle velocities studied. This behavior is attributed to differences in bulk properties and shock front structure in hydrogels with different polymer/water concentrations.

Comparison of Magnetic and Plasma Overshoots of Interplanetary Shocks

The structure of interplanetary shock fronts was studied based on the data from the BMSW plasma spectrometer, installed on the SPEKTR-R spacecraft, supplemented by magnetic field measurements on the WIND spacecraft. Special attention was paid to periodic growths (overshoots) in the value of the ion flux or magnetic field relative to their mean values outside the ramp. A comparison was performed with the overshoot in the magnetic field, with the Mach number, and with the β parameter. Based on an analysis of 18 intersections of interplanetary shock fronts, in which the overshoots in the ion flux and magnetic field value were observed, it was shown that the value of the magnetic field overshoot is, on the average, less than a similar value in the solar wind’s ion flux, which is associated with different time resolution of measurements. The ion flux overshoot value is found to grow with the growth of the Mach number, in the same way, as the value of the magnetic field overshoot. It is shown that overshoots are formed not only in the supercritical shocks, but also in those with Mach numbers that are less than the value of the first critical Mach number. It is also found that the estimates of the wavelength of the ion flux and magnetic field oscillations behind the ramp well correlate with the value of a gyroradius of captured ions.

Dynamics of bond breaking and formation in polyethylene near shock front.

In a systematic study of shock wave propagating in crystalline polyethylenes using molecular dynamics method and the electron force field (eFF) potential, we show that microscopic structure of shock front is significantly affected by the anisotropy of long carbon chain and the bond breaking and recombination dynamics. However, macroscopic properties measured in Hugoniot experiments, such as compression ratio and shock velocity, are not sensitive to carbon chain anisotropy and bond dynamics. Our work also display that hydrogen molecules are formed when the piston speed is in the region between 10 km/s and 30 km/s. However, carbon-hydrogen pair distribution function does not display an indication of carbon-hydrogen phase segregation.

Numerical Simulation of a Steam Injector for Passive Residual Heat Removal

Abstract In the case of depressurization of a supercritical water-cooled reactor (SCWR), the steam pressure can be used to pump coolant back into the reactor, either by using a turbine driven pump or a steam injector. The latter option is cheaper, more robust, and requires less periodic inspections. The numerical simulation of a steam injector, however, has still been a challenge. In principle, a steam injector consists of a steam nozzle, a mixing chamber, and a diffuser. This paper describes a one-dimensional two-phase flow model simulating the flow and condensation phenomena occurring in the steam nozzle, the structure of shock fronts at the nozzle outlet, the direct contact condensation of steam with cold water in the mixing chamber, and the sudden pressure increase in the final condensation shock front. The model is based only on first principles and on the existing correlations. Correction factors adapting the model to experimental results have not been used yet. For validation, the model has been applied both to separate effect tests and to steam injector tests.

Features of the Dynamics of a Shock Excited by Fast Coronal Mass Ejections

The event on January 27, 2012 is an example of the features of the dynamics of formation of a shock, excited by a fast coronal mass ejection (CME) at a velocity higher than 2000 km/s, are investigated. The following data were used: (a) images of the Sun in the UV channel of 13.1 nm from the AIA instrument at distances of 1.0–1.4 solar radii from the Sun’s center, (b) the images of the white corona from the LASCO C2 and C3 coronographs at R ≈ 2.1–30 solar radii. Investigations indicated the validity of regularities, established earlier for the cases of relatively slow CMEs (at velocities <1500 km/s): (1) The shock front is formed, when the velocity of a leading part of a CME relative to the undisturbed solar wind becomes greater than the local Alfven velocity of wind, which corresponds to the phenomenon of “transition through the sound velocity” for magnetized plasma. (2) The change in the width of a shock front and, accordingly, in the energy dissipation mechanism occurs in a shock front from a “collisional” one, at distances from the Sun’s center lower than 10 solar radii, to a “collisionless” one, at distances greater than ten solar radii. During the event of January 27, 2012, it was possible to investigate in more detail the process of transition from the collisional to collisionless shock front. It was found that the longitudinal length of a shock front, excited by a fast CME at distances lower than 6 solar radii, increased almost 10 times as compared to a slower CME. One of the main causes for this increase, along with a high velocity, is the fact that the motion of CME has occurred in the plane of the belt of coronal streamers. It is concluded that, at distances lower than 6 solar radii, the shock front structure ahead of the CME is of “parallel” type; that is, the angle between the vector of an undisturbed magnetic field and the normal to the front was close to 0°.

Структура и параметры ударного фронта в вязком теплопроводном газовоздушном потоке горной выработки

Структура и параметры ударного фронта в вязком теплопроводном газовоздушном потоке горной выработки

Measurements of ion velocity separation and ionization in multi-species plasma shocks

The ion velocity structure of a strong collisional shock front in a plasma with multiple ion species is directly probed in laser-driven shock-tube experiments. Thomson scattering of a 263.25 nm probe beam is used to diagnose ion composition, temperature, and flow velocity in strong shocks (M∼6) propagating through low-density (ρ∼0.1 mg/cc) plasmas composed of mixtures of hydrogen (98%) and neon (2%). Within the preheat region of the shock front, two velocity populations of ions are observed, a characteristic feature of strong plasma shocks. The ionization state of the Ne is observed to change within the shock front, demonstrating an ionization-timescale effect on the shock front structure. The forward-streaming proton feature is shown to be unexpectedly cool compared to predictions from ion Fokker-Planck simulations; the neon ionization gradient is evaluated as a possible cause.

Inner Structure of CME Shock Fronts Revealed by the Electromotive Force and Turbulent Transport Coefficients in Helios-2 Observations

Abstract Electromotive force is an essential quantity in dynamo theory. During a coronal mass ejection (CME), magnetic helicity gets decoupled from the Sun and advected into the heliosphere with the solar wind. Eventually, a heliospheric magnetic transient event might pass by a spacecraft, such as the Helios space observatories. Our aim is to investigate the electromotive force, the kinetic helicity effect (α term), the turbulent diffusion (β term), and the cross-helicity effect (γ term) in the inner heliosphere below 1 au. We set up a one-dimensional model of the solar wind velocity and magnetic field for a hypothetic interplanetary CME. Because turbulent structures within the solar wind evolve much slower than this structure needs to pass by the spacecraft, we use a reduced curl operator to compute the current density and vorticity. We test our CME shock-front model against an observed magnetic transient that passes by the Helios-2 spacecraft. At the peak of the fluctuations in this event we find strongly enhanced α, β, and γ terms, as well as a strong peak in the total electromotive force. Our method allows us to automatically identify magnetic transient events from any in situ spacecraft observations that contain magnetic field and plasma velocity data of the solar wind.

Shock waves induced by a planar obstacle in a vibrated granular gas

The low value of the speed of sound in dilute granular media permits the study of the properties of supersonic flows for a wide range of Mach numbers. In this paper, we report the experimental observation of a subsonic–supersonic transition in a vibrated granular gas. The shock fronts studied are obtained by simply pushing a rectangular obstacle into the granular gas for different obstacle velocities. The supersonic regime is characterized by the formation of normal shock waves whose width increases when the Mach number decreases to values close to 1. The bimodal model proposed by Mott-Smith in the 1950s provides a good description for the velocity distributions as well as the macroscopic quantities for shock waves in molecular gases but remains inadequate for dissipative media like granular gases and plasmas. Here by examining the shock front structure for a wide range of Mach numbers, we adapt the Mott-Smith bimodal description to a dissipative medium. By using balance equations from granular kinetic theory and taking into account different dissipation sources, the proposed model allows us to understand how this dissipation modifies temperature, mean velocity and volume fraction profiles through the shock front.

Highly Resolved Measurements of a Developing Strong Collisional Plasma Shock.

The structure of a strong collisional shock front forming in a plasma is directly probed for the first time in laser-driven gas-jet experiments. Thomson scattering of a 526.5nm probe beam was used to diagnose temperature and ion velocity distribution in a strong shock (M∼11) propagating through a low-density (ρ∼0.01 mg/cc) plasma composed of hydrogen. A forward-streaming population of ions traveling in excess of the shock velocity was observed to heat and slow down on an unmoving, unshocked population of cold protons, until ultimately the populations merge and begin to thermalize. Instabilities are observed during the merging, indicating a uniquely plasma-phase process in shock front formation.

Fine structure of interplanetary shock fronts from the data of the BMSW instrument of the PLASMA-F experiment

The paper is concerned with studying the thickness of fronts of 38 interplanetary shocks detected by the BMSW instrument, which is a part of the scientific payload of the SPEKTR-R spacecraft, which was launched into a highly elliptical orbit in 2011. The main parameters of the interplanetary shocks have been calculated as follows: the ratio of thermal pressure to magnetic pressure before the front β, the angle between the shock front normal and the undisturbed magnetic field θBn, the ratio of the shock propagation velocity to the magnetosonic velocity in the undisturbed region Mms, and the shock front velocity relative to the Earth. It has been shown that the front thickness determined from the plasma parameters approximately matches the front thickness obtained from the magnetic field measurements and lies between 0.5 and 5 proton inertial lengths. In some events, the oscillations have been observed (upstream and downstream of the shock) in plasma parameters and in the magnetic field data. The length has been found to be between 0.5 and 6 proton inertial lengths for the preceding oscillations and between 0.5 and 10 proton inertial lengths for the following oscillations. The average value of the proton inertial length is 62 km.

Fine structure of the interplanetary shock front according to measurements of the ion flux of the solar wind with high time resolution

According to the data of the BMSW/SPEKTR-R instrument, which measured the density and velocity of solar wind plasma with a record time resolution, up to ~3 ×10–2 s, the structure of the front of interplanetary shocks has been investigated. The results of these first investigations were compared with the results of studying the structure of the bow shocks obtained in previous years. A comparison has shown that the quasi-stationary (averaged over the rapid oscillations) distribution of plasma behind the interplanetary shock front was significantly more inhomogeneous than that behind the bow-shock front, i.e., in the magnetosheath. It has also been shown that, to determine the size of internal structures of the fronts of quasi-perpendicular (θBN > 45°) shocks, one could use the magnetic field magnitude, the proton density, and the proton flux of the solar wind on almost equal terms. A comparison of low Mach (МА < 2), low beta (β1 < 1) fronts of interplanetary and bow shocks has shown that the dispersion of oblique magnetosonic waves plays an essential role in their formation.