A model for the atmospheric shock wave produced by a strong volcanic explosion

2020 ◽  
Vol 222 (2) ◽  
pp. 735-742
Author(s):  
Michele Dragoni ◽  
Dalila Santoro
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Sound Pressure ◽  
Strong Shock ◽  
Weak Shock ◽  
Volcanic Eruptions ◽  
Density Inhomogeneity ◽  
Acoustic Effect ◽  
Explosive Volcanic Eruptions ◽  
Spherical Shock

SUMMARY Atmospheric shock waves are a common phenomenon in explosive volcanic eruptions. We consider the motion of a spherical shock wave generated by a point source in the strong shock approximation. The shock front corresponds to discontinuities in the gas velocity, density, pressure and temperature, which are calculated as functions of the energy of the explosion. The problem is solved analytically for the distributions of velocity, density, pressure and temperature in the atmosphere as functions of the distance from the source. The motion of the shock wave being supersonic, the solution is valid for a few seconds after the explosion, corresponding to a distance of few kilometres. The acoustic effect of the shock wave, expressed by the peak sound pressure level, is calculated and may reach hundreds of decibels. The pressure waveform that could be recorded in the vicinity of the volcano is calculated and compared with typical waveforms in weak shock conditions. The change in the refractive index of air due to density inhomogeneity is calculated and the conditions under which a condensation cloud is formed behind the shock front are investigated.

The determination of arc temperatures from shock velocities

1957 ◽  
Vol 240 (1220) ◽  
pp. 54-66 ◽  
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Wave Theory ◽  
New Method ◽  
Shock Propagation ◽  
Plane Shock ◽  
Gas Temperature ◽  
Specific Heats ◽  
Arc Discharges

The measurement of the high gas temperatures associated with arc discharges requires special techniques. One such method, developed by Suits (1935), depends on the measure­ment of the velocity of a sound wave passing through an arc column, although in fact Suits measured the velocity of a very weak shock wave. The new method described in the present paper is one in which temperatures are determined from the measurement of the velocity of a relatively strong shock wave propagated through an arc. The new method has the merit of consistently producing accurately measurable records and of increasing the accuracy of the temperature determination. The shock velocities are measured by means of a rotating mirror camera. Within the arc, the shock propagation is observable by virtue of the increased arc brightness produced by the shock. In the non-luminous regions surrounding the arc, the shock propagation is displayed by means of a Schlieren system. The interpretation of the measurements depends upon a one-dimensional analysis given in this paper which is similar to that of Chisnell (1955) and which describes the interaction of a plane shock with a con­tinuously varying temperature distribution. In our analysis account is taken also of the continuous variation in specific heats and molecular weight which are of importance under high gas temperature conditions. In practice plane wave theory cannot adequately describe the shock propagation, since attenuation occurs both in the free gas and in the arc column. The effects of this attenuation on the temperature determinations may be accounted for by the use of an experimentally determined attenuation relationship given in the paper. The finally developed method yields temperature values to an accuracy of ± 2%. Experiments are described for carbon and tungsten arcs in air and nitrogen for currents up to 55 amperes and pressures up to 3 atmospheres. The values obtained range from 6200 to 7700° K and are in good agreement with values determined by other techniques.

scholarly journals Non-linear weak shock diffraction

1968 ◽  
Vol 8 (4) ◽  
pp. 737-754 ◽  
Author(s):  
N. J. De Mestre
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Shadow Region ◽  
Ray Theory ◽  
Perturbation Expansions ◽  
Shock Diffraction ◽  
Non Linear ◽  
Flow Variables

AbstractPerturbation expansions are sought for the flow variables associated with the diffraction of a plane weak shock wave around convex-angled corners in a polytropic, inviscid, thermally-nonconducting gas. Lighthill's method of strained co-ordinates [4] produces a uniformly valid expansion for most of the diffracted front, while the remainder of this front is treated by a modification of the shock-ray theory of Whitham [6]. The solutions from these approaches are patched just inside the ‘shadow’ region yielding a plausible description of the entire diffracted shock front.

scholarly journals An Exact Analytical Solution of the Strong Shock Wave Problem in Nonideal Magnetogasdynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
S. D. Ram ◽  
R. Singh ◽  
L. P. Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Shock Front ◽  
Total Energy ◽  
Wave Motion ◽  
Exact Analytical Solution ◽  
Strong Shock ◽  
Strong Shock Wave ◽  
Wave Problem

We construct the solutions to the strong shock wave problem with generalized geometries in nonideal magnetogasdynamics. Here, it is assumed that the density ahead of the shock front varies according to a power of distance from the source of the disturbance. Also, an analytical expression for the total energy carried by the wave motion in nonideal medium under the influence of magnetic field is derived.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

1993 ◽  
Vol 251 ◽  
pp. 533-562 ◽  
Author(s):  
Sangsan Lee ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Shock Waves ◽  
Shock Front ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Isotropic Turbulence ◽  
Weak Shock ◽  
Linear Analysis ◽  
Weak Shock Wave

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number Mt of the upstream turbulence and the shock strength M21 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ Mt ≤ 0.110 and 1.05 ≤ M1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations.Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M2t < a(M21 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term.Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M2t < a(M21— 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M2t > a(M21— 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

Stability of a supersonic flow over a wedge containing a weak shock wave satisfying the Lopatinski condition

2014 ◽  
Vol 11 (02) ◽  
pp. 215-248 ◽  
Author(s):  
A. M. Blokhin ◽  
D. L. Tkachev
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Wave Solution ◽  
Strong Shock ◽  
Weak Shock ◽  
Weak Sense ◽  
Strong Shock Wave ◽  
Weak Shock Wave ◽  
Heat Conducting ◽  
Shock Wave Solution

We study the stability problem for a stationary supersonic flow of inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, this problem has two solutions: a solution with a strong shock wave (when the velocity behind the front of the shock wave is subsonic) and a solution with a weak shock wave (when the velocity behind the front of the shock wave is supersonic). We consider the case of a weak shock wave and we prove that if the Lopatinski condition for the shock wave holds (in a weak sense), then the corresponding linearized initial boundary-value problem is well-posed. We thus find a classical solution to this problem. Unlike the case when the uniform Lopatinski condition holds, additional plane waves appear. For compactly supported initial data we show that the solution of the linearized problem converges to the zero solution as time tends to infinity. Therefore, for the case of a weak shock wave and when the Lopatinski condition holds in a weak sense, these results complete the proof of the well-known Courant–Friedrichs' conjecture that the strong shock wave solution is unstable whereas the weak shock wave solution is stable.

scholarly journals Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

2010 ◽  
Vol 199 ◽  
pp. 151-181 ◽  
Author(s):  
Gang Xu ◽  
Huicheng Yin
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Vertex Angle ◽  
Transonic Shock ◽  
Euler Flow ◽  
Flow Past ◽  
Curve Method ◽  
Sharp Cone ◽  
Supersonic Shock

AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the book Supersonic Flow and Shock Waves by Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

scholarly journals Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

2010 ◽  
Vol 199 ◽  
pp. 151-181 ◽  
Author(s):  
Gang Xu ◽  
Huicheng Yin
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Vertex Angle ◽  
Transonic Shock ◽  
Euler Flow ◽  
Flow Past ◽  
Curve Method ◽  
Sharp Cone ◽  
Supersonic Shock

AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the bookSupersonic Flow and Shock Wavesby Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

Stability condition for strong shocks in flows over an infinite planar wedge satisfying the Lopatinski condition

2015 ◽  
Vol 12 (04) ◽  
pp. 817-847 ◽  
Author(s):  
A. M. Blokhin ◽  
D. L. Tkachev
Keyword(s):  
Initial Data ◽  
Shock Front ◽  
Sound Speed ◽  
Plane Waves ◽  
Classical Problem ◽  
Strong Shock ◽  
Weak Shock ◽  
Heat Conducting ◽  
Gas Velocity ◽  
Thermodynamical Equilibrium

We study the classical problem for a flow of uniform inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, theoretically this problem has solutions of two types. Solutions of the first type correspond to a strong shock when the gas velocity behind the shock front is less than the sound speed whereas solutions of the second type correspond to the case of a weak shock when the gas velocity behind the shock front is greater than the sound speed. The shock fronts are attached to the wedge vertex. We consider the linear problem for a strong shock wave provided that the Lopatinski condition holds (in a weak sense) on the shock front and the initial data are compactly, i.e. supports of the initial data are separated from the coordinate axes. Under some additional conditions on the initial data we find a solution of the generalized problem. In contrast to the previously studied case when the uniform Lopatinski condition holds on the shock front, this solution contains plane waves. The stability of the found solution is thus justified on the linear level what gives a principle possibility to realize the flow regime containing a strong shock as time increases.

The initial ionization of hydrogen in a strong shock wave

1969 ◽  
Vol 36 (4) ◽  
pp. 695-720 ◽  
Author(s):  
A. N. Belozerov ◽  
R. M. Measures
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Cross Section ◽  
Theoretical Calculations ◽  
Strong Shock ◽  
Operating Conditions ◽  
Strong Shock Wave ◽  
Relaxation Length ◽  
Single Temperature ◽  
The Cross

A theoretical and experimental investigation has been made of the initial ionization processes in a strong shock wave in hydrogen. The relaxation length for ionization, which is principally determined by the rate of excitation, was measured and from a comparison with the theory an estimate was obtained for the cross-section for atom-atom excitation collisions.Detailed theoretical calculations showed that the electron temperature approaches to within 1 % of the atomic temperature in a distance that is small compared with the total relaxation length for ionization. This enabled considerable simplification, for it indicated that a single-temperature model could be used in calculating the theoretical relaxation profile over the experimental range of operating conditions. An electromagnetic shock tube, with a Philippov pinch to create the driver plasma, was employed to produce shock waves of the required velocity. The ionization behind the shock front was studied by means of a double-frequency Mach-Zehnder interferometer, with a ruby laser and a K.D.P. crystal as the light source. A close agreement between the theoretical and experimental electron density profiles, behind the shock front, was obtained for small relaxation lengths, when the cross-section for the atom-atom excitation collisions was assumed to be about 7 × 10−2 times that of the corresponding cross-section for electron-atom excitation collisions.

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