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continuous and the density is discontinuous. A strong expansion wave or shear layer may also contain high gradient regions which appear to be a discontinuity. Some common features of these flow structures and shock waves and the insufficient aspects of numerical and experimental tools lead to two important problems in practices: (1) some shock waves can not be detected or their positions are detected wrong, (2) some flow structures which are not shock waves are wrongly detected to be shock waves.
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lower surface of the vehicle can produce high pressure to generate lift, (3) leading to wave drag of high-speed vehicle which is harmful to vehicle performance, (4) inducing severe pressure load and heat flux, e.g. the Type IV shock–shock interference could yield a 17 times heating increase at vehicle surface, (5) interacting with other structures, such as boundary layers, to produce new flow structures such as flow separation, transition, etc.
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They are a topic of continuing interest, because the rules governing the shock's distance ahead of the blunt body are complicated and are a function of the body's shape. Additionally, the shock standoff distance varies drastically with the temperature for a non-ideal gas, causing large differences in the heat transfer to the thermal protection system of the vehicle. See the extended discussion on this topic at
335:) change almost instantaneously. Measurements of the thickness of shock waves in air have resulted in values around 200 nm (about 10 in), which is on the same order of magnitude as the mean free path of gas molecules. In reference to the continuum, this implies the shock wave can be treated as either a line or a plane if the flow field is two-dimensional or three-dimensional, respectively.
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358:–Meyer compressions. The method of compression of a gas results in different temperatures and densities for a given pressure ratio which can be analytically calculated for a non-reacting gas. A shock wave compression results in a loss of total pressure, meaning that it is a less efficient method of compressing gases for some purposes, for instance in the intake of a
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leaving the aircraft pile up on one another, similar to a traffic jam on a motorway. When a shock wave forms, the local air pressure increases and then spreads out sideways. Because of this amplification effect, a shock wave can be very intense, more like an explosion when heard at a distance (not coincidentally, since explosions create shock waves).
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pressure levels in brass instruments such as the trombone become high enough for steepening to occur, forming an essential part of the bright timbre of the instruments. While shock formation by this process does not normally happen to unenclosed sound waves in Earth's atmosphere, it is thought to be one mechanism by which the
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separation of the boundary layer at the point where it touches the transonic profile. This can then lead to full separation and stall on the profile, higher drag, or shock-buffet, a condition where the separation and the shock interact in a resonance condition, causing resonating loads on the underlying structure.
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Shock waves can also occur in rapid flows of dense granular materials down inclined channels or slopes. Strong shocks in rapid dense granular flows can be studied theoretically and analyzed to compare with experimental data. Consider a configuration in which the rapidly moving material down the chute
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on the shore. In shallow water, the speed of surface waves is dependent on the depth of the water. An incoming ocean wave has a slightly higher wave speed near the crest of each wave than near the troughs between waves, because the wave height is not infinitesimal compared to the depth of the water.
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When analyzing shock waves in a flow field, which are still attached to the body, the shock wave which is deviating at some arbitrary angle from the flow direction is termed oblique shock. These shocks require a component vector analysis of the flow; doing so allows for the treatment of the flow in
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Shadowgram of shock waves from a supersonic bullet fired from a rifle. The shadowgraph optical technique reveals that the bullet is moving at about a Mach number of 1.9. Left- and right-running bow waves and tail waves stream back from the bullet and its turbulent wake is also visible. Patterns at
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is established around the shock wave, with the control surfaces that bound this volume parallel to the shock wave (with one surface on the pre-shock side of the fluid medium and one on the post-shock side). The two surfaces are separated by a very small depth such that the shock itself is entirely
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In fact, correct capturing and detection of shock waves are important since shock waves have the following influences: (1) causing loss of total pressure, which may be a concern related to scramjet engine performance, (2) providing lift for wave-rider configuration, as the oblique shock wave at
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These shocks are curved and form a small distance in front of the body. Directly in front of the body, they stand at 90 degrees to the oncoming flow and then curve around the body. Detached shocks allow the same type of analytic calculations as for the attached shock, for the flow near the shock.
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is commonly used to obtain the flow field with shock waves. Though shock waves are sharp discontinuities, in numerical solutions of fluid flow with discontinuities (shock wave, contact discontinuity or slip line), the shock wave can be smoothed out by low-order numerical method (due to numerical
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The attached shock wave is a classic structure in aerodynamics because, for a perfect gas and inviscid flow field, an analytic solution is available, such that the pressure ratio, temperature ratio, angle of the wedge and the downstream Mach number can all be calculated knowing the upstream Mach
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To produce a shock wave, an object in a given medium (such as air or water) must travel faster than the local speed of sound. In the case of an aircraft travelling at high subsonic speed, regions of air around the aircraft may be travelling at exactly the speed of sound, so that the sound waves
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in gas or plasma, due to the dependence of the sound speed on temperature and pressure. Strong waves heat the medium near each pressure front, due to adiabatic compression of the air itself, so that high pressure fronts outrun the corresponding pressure troughs. There is a theory that the sound
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Taking into account the established assumptions, in a system where the downstream properties are becoming subsonic: the upstream and downstream flow properties of the fluid are considered isentropic. Since the total amount of energy within the system is constant, the stagnation enthalpy remains
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Shock waves are formed when a pressure front moves at supersonic speeds and pushes on the surrounding air. At the region where this occurs, sound waves travelling against the flow reach a point where they cannot travel any further upstream and the pressure progressively builds in that region; a
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Where the flow over the suction side of a transonic wing is accelerated to a supersonic speed, the resulting re-compression can be by either
Prandtl–Meyer compression or by the formation of a normal shock. This shock is of particular interest to makers of transonic devices because it can cause
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number and the shock angle. Smaller shock angles are associated with higher upstream Mach numbers, and the special case where the shock wave is at 90° to the oncoming flow (Normal shock), is associated with a Mach number of one. These follow the "weak-shock" solutions of the analytic equations.
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In this case, the gas ahead of the shock is stationary (in the laboratory frame) and the gas behind the shock can be supersonic in the laboratory frame. The shock propagates with a wavefront which is normal (at right angles) to the direction of flow. The speed of the shock is a function of the
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A shock wave may be described as the furthest point upstream of a moving object which "knows" about the approach of the object. In this description, the shock wave position is defined as the boundary between the zone having no information about the shock-driving event and the zone aware of the
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Shock waves are not conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties. Shock waves in air are heard as a loud "crack" or "snap" noise. Over longer distances, a shock wave can change from a nonlinear wave into a linear wave, degenerating into a
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There exist some other discontinuities in fluid flow than the shock wave. The slip surface (3D) or slip line (2D) is a plane across which the tangent velocity is discontinuous, while pressure and normal velocity are continuous. Across the contact discontinuity, the pressure and velocity are
884:) (Although for some oblique shocks very close to the deflection angle limit, the downstream Mach number is subsonic.) The shock is the result of the deceleration of the gas by a converging duct, or by the growth of the boundary layer on the wall of a parallel duct.
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A detonation wave follows slightly different rules from an ordinary shock since it is driven by the chemical reaction occurring behind the shock wavefront. In the simplest theory for detonations, an unsupported, self-propagating detonation wave proceeds at the
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When an object (or disturbance) moves faster than the information can propagate into the surrounding fluid, then the fluid near the disturbance cannot react or "get out of the way" before the disturbance arrives. In a shock wave the properties of the fluid
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Pressure–time diagram at an external observation point for the case of a supersonic object propagating past the observer. The leading edge of the object causes a shock (left, in red) and the trailing edge of the object causes an expansion (right, in
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Contact front: In a shock wave caused by a driver gas (for example the "impact" of a high explosive on the surrounding air), the boundary between the driver (explosive products) and the driven (air) gases. The contact front trails the shock
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thin layer to a stagnant thick heap. This flow configuration is particularly interesting because it is analogous to some hydraulic and aerodynamic situations associated with flow regime changes from supercritical to subcritical flows.
423:
When an oblique shock is likely to form at an angle which cannot remain on the surface, a nonlinear phenomenon arises where the shock wave will form a continuous pattern around the body. These are termed
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are usually generated by the interaction of two bodies of gas at different pressure, with a shock wave propagating into the lower pressure gas and an expansion wave propagating into the higher pressure
1283:
Silber E.A., Boslough M., Hocking W.K., Gritsevich M., Whitaker R.W. (2018). Physics of Meteor
Generated Shock Waves in the Earth's Atmosphere – A Review. Advances in Space Research, 62(3), 489-532
647:. These follow the "strong-shock" solutions of the analytic equations, meaning that for some oblique shocks very close to the deflection angle limit, the downstream Mach number is subsonic. See also
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The crests overtake the troughs until the leading edge of the wave forms a vertical face and spills over to form a turbulent shock (a breaker) that dissipates the wave's energy as sound and heat.
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colliding with each other. Another interesting type of shock in astrophysics is the quasi-steady reverse shock or termination shock that terminates the ultra relativistic wind from young
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Proceedings of
Symposium on the Behavior of Dense Media Under High Dynamic Pressure. (Éditions du Commissariat à l'Énergie Atomique, Centre d'Études Nucléaires de Saclay, Paris)
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Such a shock occurs when the maximum deflection angle is exceeded. A detached shock is commonly seen on blunt bodies, but may also be seen on sharp bodies at low Mach numbers.
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Tang, Shao; Tesler, Federico; Marlasca, Fernando Gomez; Levy, Pablo; Dobrosavljević, V.; Rozenberg, Marcelo (2016-03-15). "Shock Waves and
Commutation Speed of Memristors".
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during training exercises in Puerto Rico, 1984. Circular marks are visible where the expanding spherical atmospheric shockwaves from the gun firing meet the water surface.
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in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in
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1129:
Landau, L. D., & Lifshitz, E. M. (1987). Fluid
Mechanics, Volume 6 of course of theoretical physics. Course of theoretical physics/by LD Landau and EM Lifshitz, 6.
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impinges on an obstruction wall erected perpendicular at the end of a long and steep channel. Impact leads to a sudden change in the flow regime from a fast moving
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can be modelled as heat introduction across a shock wave. It is assumed the system is adiabatic (no heat exits or enters the system) and no work is being done. The
214:(another kind of nonlinear wave), the energy and speed of a shock wave alone dissipates relatively quickly with distance. When a shock wave passes through matter,
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When the 2013 meteor entered into the Earth's atmosphere with an energy release equivalent to 100 or more kilotons of TNT, dozens of times more powerful than the
917:, under externally-applied electric field, shock waves can be launched across the transition-metal oxides, creating fast and non-volatile resistivity changes.
399:
199:. The accompanying expansion wave may approach and eventually collide and recombine with the shock wave, creating a process of destructive interference. The
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Krehl, Peter O. K. (2011), "Shock wave physics and detonation physics — a stimulus for the emergence of numerous new branches in science and engineering",
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Nikonov, V. A Semi-Lagrangian
Godunov-Type Method without Numerical Viscosity for Shocks. Fluids 2022, 7, 16. https://doi.org/10.3390/fluids7010016
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Nikonov, V. A Semi-Lagrangian
Godunov-Type Method without Numerical Viscosity for Shocks. Fluids 2022, 7, 16. https://doi.org/10.3390/fluids7010016
428:. In these cases, the 1d flow model is not valid and further analysis is needed to predict the pressure forces which are exerted on the surface.
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constant over both regions. However, entropy is increasing; this must be accounted for by a drop in stagnation pressure of the downstream fluid.
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to transfer energy between a high-energy fluid to a low-energy fluid, thereby increasing both temperature and pressure of the low-energy fluid.
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Advanced techniques are needed to capture shock waves and to detect shock waves in both numerical computations and experimental observations.
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673:, the detached shock formed at the bow (front) of a ship or boat moving through water, whose slow surface wave speed is easily exceeded (see
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In this case the gas ahead of the shock is supersonic (in the laboratory frame), and the gas behind the shock system is either supersonic (
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flow velocity. A detonation will also cause a shock to propagate into the surrounding air due to the overpressure induced by the explosion.
378:, a shock wave is treated as a discontinuity where entropy increases abruptly as the shock passes. Since no fluid flow is discontinuous, a
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increases. This change in the matter's properties manifests itself as a decrease in the energy which can be extracted as work, and as a
1120:
Zel'Dovich, Y. B., & Raizer, Y. P. (2012). Physics of shock waves and high-temperature hydrodynamic phenomena. Courier
Corporation.
610:
583:. The chemical reaction of the medium occurs following the shock wave, and the chemical energy of the reaction drives the wave forward.
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In the examples below, the shock wave is controlled, produced by (ex. airfoil) or in the interior of a technological device, like a
93:
71:
579:. It involves a wave travelling through a highly combustible or chemically unstable medium, such as an oxygen-methane mixture or a
759:
307:: the pressure–time diagram of a supersonic object propagating shows how the transition induced by a shock wave is analogous to a
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Courant, R., & Friedrichs, K. O. (1999). Supersonic flow and shock waves (Vol. 21). Springer
Science & Business Media.
350:
The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. Some other methods are
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Shapiro, A. H. (1953). The dynamics and thermodynamics of compressible fluid flow, vol. 1 (Vol. 454). Ronald Press, New York.
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conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a
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dissipation) or there are spurious oscillations near shock surface by high-order numerical method (due to Gibbs phenomena).
588:
797:, with the circular shock wave centred at the meteor explosion, causing multiple instances of broken glass in the city of
1659:
Hoover, Wm. G.; Hoover, Carol G.; Travis, Karl P. (10 April 2014). "Shock-Wave
Compression and Joule-Thomson Expansion".
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Shock wave propagating into a stationary medium, ahead of the fireball of an explosion. The shock is made visible by the
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362:. The appearance of pressure-drag on supersonic aircraft is mostly due to the effect of shock compression on the flow.
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contained between them. At such control surfaces, momentum, mass flux and energy are constant; within combustion,
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Shock front: The boundary over which the physical conditions undergo an abrupt change because of a shock wave.
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Analogous phenomena are known outside fluid mechanics. For example, charged particles accelerated beyond the
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Veeser, L.; Solem, J. C.; Lieber, A. (1979). "Impedance-match experiments using laser-driven shock waves".
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The abruptness of change in the features of the medium, that characterize shock waves, can be viewed as a
75:
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of the detached shock on a bullet in supersonic flight, published by Ernst Mach and Peter Salcher in 1887
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Shock waves can form due to steepening of ordinary waves. The best-known example of this phenomenon is
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Veeser, L.; Lieber, A.; Solem, J. C. (1979). "Planar streak camera laser-driven shockwave studies".
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Astrophysical environments feature many different types of shock waves. Some common examples are
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of 6,900 m/s), it will always travel at high, supersonic velocity from its point of origin.
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Below are a number of examples of shock waves, broadly grouped with similar shock phenomena:
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Wu ZN, Xu YZ, etc (2013), "Review of shock wave detection method in CFD post-processing",
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Liepman, H. W., & Roshko, A. (1957). Elements of gas dynamics. John Willey & Sons.
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These shocks appear when the flow over a transonic body is decelerated to subsonic speeds.
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associated with the passage of a supersonic aircraft is a type of sound wave produced by
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Veeser, L. R.; Solem, J. C. (1978). "Studies of Laser-driven shock waves in aluminum".
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Settles, Gary S. (2006). "High-speed Imaging of Shock Wave, Explosions and Gunshots".
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Shock waves are generated by meteoroids when they enter the Earth's atmosphere. The
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Examples: Space return vehicles (Apollo, Space shuttle), bullets, the boundary (
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1638:. San Diego, California: California Technical Publishing. pp. 209–224.
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Hirschberg, A.; Gilbert, J.; Msallam, R.; Wijnands, A. P. J. (March 1996),
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17:
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the far right are from unburned gunpowder particles ejected by the rifle.
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Conical shockwave with its hyperbola-shaped ground contact zone in yellow
173:
1719:
1635:
Digital Signal Processing a Practical Guide for Engineers and Scientists
1165:
168:, is a type of propagating disturbance that moves faster than the local
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Solem, J. C.; Veeser, L. R. (1978). "Laser-driven shock wave studies".
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Usually consists of a shock wave propagating into a stationary medium
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215:
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Selkirk college: Aviation intranet: High speed (supersonic) flight
265:) of a blunt object when the upstream flow velocity exceeds Mach 1.
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1310:
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897:(also named "Radial Internal Combustion Wave Rotor") is a kind of
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138:
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105:
1488:(Los Alamos Scientific Laboratory Report LA-UR-78-1039): 463–476.
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This shock appears when supersonic flow in a pipe is decelerated.
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are the best documented evidence of the shock wave produced by a
464:
are heated, via waves that propagate up from the solar interior.
191:
flows, additional increased expansion may be achieved through an
496:(such as water, where the speed of light is less than that in a
415:
an orthogonal direction to the oblique shock as a normal shock.
152:
that rocketed across the Russian morning sky on 15 February 2013
37:"Bombshock" redirects here. For the Transformers character, see
825:
Recompression shock on a transonic-flow airfoil, at and above
454:
43:
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jet's flyby (directly underneath the meteor's path) and as a
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Examples: Supersonic wedges and cones with small apex angles.
245:
At 90° (perpendicular) to the shock medium's flow direction.
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Energy loss in a shock wave, normal and oblique shock waves
1537:
Impedance-match experiments using laser-driven shock waves
347:, commonly created by the supersonic flight of aircraft.
933:
of shock waves interacting between two aircraft in 2019.
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caused by the Earth's magnetic field colliding with the
691:
to the tip of sharp bodies moving at supersonic speeds.
537:
original pressure ratio between the two bodies of gas.
500:) create visible shock effects, a phenomenon known as
1599:
Proceedings of International Conference on Lasers '79
1177:
Fox, Robert W.; McDonald, Alan T. (20 January 1992).
575:
wave is essentially a shock supported by a trailing
789:, the meteor's shock wave produced damages as in a
669:. The name "bow shock" comes from the example of a
735:travelling through the interstellar medium, the
30:"Shockwave" redirects here. For other uses, see
1408:Los Alamos Scientific Laboratory Report LA-6997
871:In flow control: needle valve, choked venturi.
1534:Solem, J. C.; Veeser, L.; Lieber, A. (1979).
1401:"Exploratory laser-driven shock wave studies"
8:
1384:: CS1 maint: multiple names: authors list (
1238:Journal of the Acoustical Society of America
400:Thermodynamic relations across normal shocks
1776:NASA Glenn Research Center information on:
1817:NASA 2015 Schlieren image shock wave T-38C
1674:
1370:
1309:
1285:https://doi.org/10.1016/j.asr.2018.05.010
94:Learn how and when to remove this message
473:shock-driving event, analogous with the
339:high-pressure shock wave rapidly forms.
285:
57:This article includes a list of general
1812:Fundamentals of compressible flow, 2007
1093:Anderson, John D. Jr. (January 2001) ,
1085:
432:Shock waves due to nonlinear steepening
1579:
1569:
1377:
113:of an attached shock on a sharp-nosed
253:At an angle to the direction of flow.
7:
1099:McGraw-Hill Science/Engineering/Math
836:Examples: Transonic wings, turbines
801:and neighbouring areas (pictured).
1540:. Vol. 35. pp. 761–763.
187:For the purpose of comparison, in
63:it lacks sufficient corresponding
25:
1399:Solem, J. C.; Veeser, L. (1977).
391:arise from these considerations.
1805:Formation of a normal shock wave
1038:Shocks and discontinuities (MHD)
787:atomic bomb dropped on Hiroshima
594:When a shock wave is created by
448:Similar phenomena affect strong
224:drag force on supersonic objects
48:
1179:Introduction To Fluid Mechanics
1693:10.1103/PhysRevLett.112.144504
1351:Chinese Journal of Aeronautics
261:Occurs upstream of the front (
1:
921:Shock capturing and detection
1095:Fundamentals of Aerodynamics
941:Computational fluid dynamics
547:Examples: Balloon bursting,
1734:European Physical Journal H
1471:10.1103/PhysRevLett.40.1391
1058:Undercompressive shock wave
1033:Prandtl–Meyer expansion fan
968:Shock waves in astrophysics
723:Shock waves in astrophysics
477:described in the theory of
389:Rankine–Hugoniot conditions
226:; shock waves are strongly
197:Prandtl–Meyer expansion fan
1848:
1755:10.1140/epjh/e2011-10037-x
1231:"Shock Waves in Trombones"
1181:(Fourth ed.). Wiley.
856:In supersonic propulsion:
805:Technological applications
743:and shock waves caused by
720:
634:
631:Bow shock (detached shock)
563:
397:
36:
32:Shockwave (disambiguation)
29:
1632:Smith, Steven W. (2003).
1372:10.1016/j.cja.2013.05.001
1328:10.1103/physrevx.6.011028
776:2013 Russian meteor event
553:shock wave from explosion
205:constructive interference
899:pistonless rotary engine
637:Bow shock (aerodynamics)
354:compressions, including
309:dynamic phase transition
1785:Multiple Crossed Shocks
1662:Physical Review Letters
1501:Applied Physics Letters
1451:Physical Review Letters
703:In rapid granular flows
687:These shocks appear as
148:The shockwave from the
78:more precise citations.
27:Propagating disturbance
934:
929:NASA took their first
829:
767:
755:Meteor entering events
627:
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300:
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228:irreversible processes
153:
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118:
1053:Supercritical airfoil
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398:Further information:
298:
289:
147:
124:
109:
998:Joule–Thomson effect
973:Atmospheric focusing
931:Schlieren photograph
827:critical Mach number
615:Schlieren photograph
523:(Trinity explosion).
238:Shock waves can be:
111:Schlieren photograph
1747:2011EPJH...36...85K
1685:2014PhRvL.112n4504H
1611:1979STIN...8024618V
1546:1979ApPhL..35..761V
1513:1979ApPhL..35..761V
1463:1978PhRvL..40.1391V
1420:1977STIN...7914376S
1363:2013ChJAn..26..501W
1320:2016PhRvX...6a1028T
1250:1996ASAJ...99.1754H
1073:Kelvin wake pattern
1018:Normal shock tables
983:Cherenkov radiation
978:Atmospheric reentry
817:Recompression shock
765:a meteor shock wave
645:atmospheric reentry
604:detonation velocity
577:exothermic reaction
502:Cherenkov radiation
282:In supersonic flows
1216:10.1511/2006.57.22
1204:American Scientist
935:
889:Combustion engines
880:s) or subsonic (a
830:
768:
675:ocean surface wave
628:
619:
525:
479:special relativity
301:
293:
269:Some other terms:
195:, also known as a
154:
150:Chelyabinsk meteor
137:
119:
1298:Physical Review X
1108:978-0-07-237335-6
1043:Shock (mechanics)
1028:Prandtl condition
780:massive meteoroid
763:Damage caused by
494:refractive medium
218:is preserved but
145:
104:
103:
96:
16:(Redirected from
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1260:, archived from
1258:10.1121/1.414698
1244:(3): 1754–1758,
1235:
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1199:
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1127:
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1111:
1097:(3rd ed.),
1090:
895:wave disk engine
508:Phenomenon types
305:phase transition
146:
99:
92:
88:
85:
79:
74:this article by
65:inline citations
52:
51:
44:
21:
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1725:Further reading
1717:
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958:
923:
911:
891:
847:
819:
807:
795:detonation wave
757:
731:shock waves or
725:
719:
717:In astrophysics
705:
684:
639:
633:
596:high explosives
589:Chapman–Jouguet
568:
562:
560:Detonation wave
530:
510:
470:
434:
421:
412:
407:
402:
372:fluid mechanics
368:
284:
236:
184:of the medium.
139:
100:
89:
83:
80:
70:Please help to
69:
53:
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1794:
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1792:
1790:Expansion Fans
1787:
1782:
1780:Oblique Shocks
1772:
1771:External links
1769:
1768:
1767:
1726:
1723:
1715:
1714:
1669:(14): 144504.
1651:
1645:978-0966017632
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1580:|journal=
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993:Hydraulic jump
990:
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957:
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907:
901:that utilizes
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772:Tunguska event
756:
753:
721:Main article:
718:
715:
704:
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695:
692:
683:
682:Attached shock
680:
679:
678:
659:
656:
635:Main article:
632:
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608:
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592:
584:
581:high explosive
564:Main article:
561:
558:
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545:
538:
534:
529:
526:
509:
506:
490:speed of light
469:
466:
433:
430:
420:
417:
411:
410:Oblique shocks
408:
406:
403:
380:control volume
370:In elementary
367:
364:
283:
280:
279:
278:
274:
267:
266:
259:
254:
251:
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243:
235:
232:
170:speed of sound
160:(also spelled
156:In physics, a
102:
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84:September 2015
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1267:on 2019-12-10
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664:
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602:(which has a
601:
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541:Moving shocks
539:
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521:shadow effect
517:
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366:Normal shocks
365:
363:
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346:
340:
336:
334:
330:
329:flow velocity
326:
322:
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288:
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272:
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233:
231:
229:
225:
221:
217:
213:
208:
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202:
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194:
193:expansion fan
190:
185:
183:
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1008:Magnetopause
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882:normal shock
881:
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458:chromosphere
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39:Micromasters
1832:Shock waves
1507:(10): 761.
903:shock waves
799:Chelyabinsk
733:blast waves
450:sound waves
438:ocean waves
385:detonations
376:ideal gases
333:Mach number
325:temperature
234:Terminology
178:temperature
76:introducing
1271:2017-04-17
1080:References
1048:Sonic boom
963:Blast wave
915:memristors
909:Memristors
853:Examples:
791:supersonic
741:solar wind
729:supernovae
573:detonation
566:Detonation
549:shock tube
475:light cone
440:that form
426:bow shocks
419:Bow shocks
374:utilizing
352:isentropic
345:sonic boom
201:sonic boom
189:supersonic
158:shock wave
131:firing at
115:supersonic
59:references
18:Shock Wave
1763:123074683
1676:1311.1717
1582:ignored (
1572:cite book
1414:: 14376.
1336:112884175
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1003:Mach wave
988:Explosion
845:Pipe flow
737:bow shock
663:bow shock
649:bow shock
468:Analogies
162:shockwave
133:broadside
1826:Category
1709:33580985
1701:24765974
1380:citation
956:See also
862:scramjet
774:and the
745:galaxies
689:attached
671:bow wave
598:such as
442:breakers
360:scramjet
321:pressure
212:solitons
174:pressure
1743:Bibcode
1681:Bibcode
1619:5806611
1607:Bibcode
1542:Bibcode
1509:Bibcode
1459:Bibcode
1436:5313279
1416:Bibcode
1359:Bibcode
1316:Bibcode
1246:Bibcode
1063:Unstart
866:unstart
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749:pulsars
665:) of a
356:Prandtl
317:density
249:Oblique
220:entropy
210:Unlike
182:density
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462:corona
291:blue).
277:front.
242:Normal
216:energy
180:, and
164:), or
61:, but
1759:S2CID
1705:S2CID
1671:arXiv
1404:(PDF)
1332:S2CID
1306:arXiv
1265:(PDF)
1234:(PDF)
492:in a
455:solar
166:shock
1697:PMID
1640:ISBN
1615:OSTI
1584:help
1558:ISBN
1432:OSTI
1386:link
1183:ISBN
1103:ISBN
893:The
544:gas.
460:and
128:Iowa
126:USS
117:body
1751:doi
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