Shock wave
Encyclopedia
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
, it carries energy and can propagate through a medium (solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
, liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
, gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
or plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
) or in some cases in the absence of a material medium, through a field
Field (physics)
In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
such as the electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
. Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
, temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
and density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of the flow. In supersonic flows, expansion is achieved through an expansion fan. A shock wave travels through most media at a higher speed than an ordinary wave.
Unlike soliton
Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
s (another kind of nonlinear wave), the energy of a shock wave dissipates relatively quickly with distance. Also, the accompanying expansion wave approaches and eventually merges with the shock wave, partially cancelling it out. Thus the sonic boom
Sonic boom
A sonic boom is the sound associated with the shock waves created by an object traveling through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion...
associated with the passage of a supersonic aircraft is the sound wave resulting from the degradation and merging of the shock wave and the expansion wave produced by the aircraft.
When a shock wave passes through matter, the total energy is preserved but the energy which can be extracted as work decreases and entropy increases. This, for example, creates additional drag
Wave drag
In aeronautics, wave drag is a component of the drag on aircraft, blade tips and projectiles moving at transonic and supersonic speeds, due to the presence of shock waves. Wave drag is independent of viscous effects.- Overview :...
force on aircraft with shocks.
Terminology
Shock waves can be:- Normal: at 90° (perpendicular) to the shock medium's flow direction.
- ObliqueOblique shockAn oblique shock wave, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave...
: at an angle to the direction of flow. - BowBow shock (aerodynamics)A bow shock, also called a detached shock, is a curved, stationary shock wave that is found in supersonic flow past a finite body. Unlike an oblique shock, the bow shock is not necessarily attached to the tip of the body...
: Occurs upstream of the front (bowBow (ship)The bow is a nautical term that refers to the forward part of the hull of a ship or boat, the point that is most forward when the vessel is underway. Both of the adjectives fore and forward mean towards the bow...
) of a blunt object when the upstream velocity exceeds Mach 1.
Some other terms
- Shock Front: an alternative name for the shock wave itself
- 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 Front.
In supersonic flows
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
, temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
, Mach number
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
) change almost instantaneously. Measurements of the thickness of shock waves have resulted in values approximately one order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
greater than the mean free path
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
of the gas investigated.
Shock waves form when the speed of a gas changes by more than the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
. At the region where this occurs sound waves traveling against the flow reach a point where they cannot travel any further upstream and the pressure progressively builds in that region, and a high pressure shock wave rapidly forms.
Shock waves are not conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties on the order of a few mean free path
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
s (roughly micro-meters at atmospheric conditions) in thickness. 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 conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom
Sonic boom
A sonic boom is the sound associated with the shock waves created by an object traveling through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion...
, commonly created by the supersonic
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
flight of aircraft.
The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. Some other methods are isentropic compressions, including Prandtl-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 scramjet
Scramjet
A scramjet is a variant of a ramjet airbreathing jet engine in which combustion takes place in supersonic airflow...
. The appearance of pressure-drag on supersonic aircraft is mostly due to the effect of shock compression on the flow.
Due to nonlinear steepening
Shock waves can form due to steepening of ordinary waves. The best-known example of this phenomenon is ocean waves that form breakerBreaking wave
In fluid dynamics, a breaking wave is a wave whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be transformed into turbulent kinetic energy...
s on the shore
Shore
A shore or shoreline is the fringe of land at the edge of a large body of water, such as an ocean, sea, or lake. In Physical Oceanography a shore is the wider fringe that is geologically modified by the action of the body of water past and present, while the beach is at the edge of 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. 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.
Similar phenomena affect strong sound waves in gas or plasma, due to the dependence of the sound speed on temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
and pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
. 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. While shock formation by this process does not normally happen to sound waves in Earth's atmosphere, it is thought to be one mechanism by which the solar
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
chromosphere
Chromosphere
The chromosphere is a thin layer of the Sun's atmosphere just above the photosphere, roughly 2,000 kilometers deep....
and corona
Corona
A corona is a type of plasma "atmosphere" of the Sun or other celestial body, extending millions of kilometers into space, most easily seen during a total solar eclipse, but also observable in a coronagraph...
are heated, via waves that propagate up from the solar interior.
Analogies
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 shock-driving event, analogous with the light coneLight cone
A light cone is the path that a flash of light, emanating from a single event and traveling in all directions, would take through spacetime...
described in the theory of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
.
To get a shock wave something has to be travelling faster than the local speed of sound. In that case some parts of the air around the aircraft are travelling at exactly the speed of sound with the aircraft, so that the sound waves leaving the aircraft pile up on each other, similar to a tailback
Tailback
Tailback can mean:* Halfback * A line of motor vehicles caught up in traffic congestion; a traffic jam...
on a road, and a shock wave forms, the pressure increases, and then spreads out sideways. Because of this amplification effect, a shock wave is very intense, more like an explosion when heard (not coincidentally, since explosions create shock waves).
Analogous phenomena are known outside fluid mechanics. For example, particles accelerated beyond the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in a refractive medium
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
(where the speed of light is less than that in a vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
, such as water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
) create visible shock effects, a phenomenon known as Cherenkov radiation
Cherenkov radiation
Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...
.
Examples
Below are a number of examples of shock waves, broadly grouped with similar shock phenomena:
Moving shock
- Usually consists of a shockwave propagating into a stationary medium
- In this case, the gas ahead of the shock is stationary (in the laboratory frame), and the gas behind the shock is supersonic in the laboratory frame. The shock propagates with a wave front which is normal (at right angles) to the direction of flow. The speed of the shock is a function of the original pressure ratio between the two bodies of gas.
- Moving shockMoving shockIn fluid dynamics, a moving shock is a shock wave that is traveling through a fluid medium with a velocity relative to the velocity of the fluid already making up the medium. As such, the normal shock relations require modification to calculate the properties before and after the moving shock...
s 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 gas. - Examples: Balloon bursting, Shock tubeShock tubeFor the pyrotechnic initiator, see Shock tube detonatorThe shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale...
, shock wave from explosionBlast waveA blast wave in fluid dynamics is the pressure and flow resulting from the deposition of a large amount of energy in a small very localised volume. The flow field can be approximated as a lead shock wave, followed by a 'self-similar' subsonic flow field. In simpler terms, a blast wave is an area of...
Detonation wave
- A detonationDetonationDetonation involves a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations are observed in both conventional solid and liquid explosives, as well as in reactive gases...
wave is essentially a shock supported by a trailing exothermic reactionExothermic reactionAn exothermic reaction is a chemical reaction that releases energy in the form of light or heat. It is the opposite of an endothermic reaction. Expressed in a chemical equation:-Overview:...
. It involves a wave traveling through a highly combustible or chemically unstable medium, such as an oxygen-methane mixture or a high explosive. The chemical reaction of the medium occurs following the shock wave, and the chemical energy of the reaction drives the wave forward. - A detonation wave follows slightly different rules from an ordinary shock since it is driven by the chemical reaction occurring behind the shock wave front. In the simplest theory for detonations, an unsupported, self-propagating detonation wave proceeds at the Chapman-JouguetChapman-Jouguet conditionThe Chapman–Jouguet condition holds approximately in detonation waves in high explosives. It states that the detonation propagates at a velocity at which the reacting gases just reach sonic velocity as the reaction ceases....
velocity. A detonation will also cause a shock of type 1, above to propagate into the surrounding air due to the overpressure induced by the explosion. - When a shockwave is created by high explosives such as TNT (which has a detonation velocity of 6,900 m/s), it will always travel at high, supersonicSupersonicSupersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
velocityVelocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
from its point of origin.
Detached shock
- 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. 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 Atmospheric reentryAtmospheric reentryAtmospheric entry is the movement of human-made or natural objects as they enter the atmosphere of a celestial body from outer space—in the case of Earth from an altitude above the Kármán Line,...
. 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 bow shockBow shock (aerodynamics)A bow shock, also called a detached shock, is a curved, stationary shock wave that is found in supersonic flow past a finite body. Unlike an oblique shock, the bow shock is not necessarily attached to the tip of the body...
or oblique shockOblique shockAn oblique shock wave, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave... - 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.
- Examples: Space return vehicles (Apollo, Space shuttle), bullets, the boundary (Bow shockBow shockA bow shock is the area between a magnetosphere and an ambient medium. For stars, this is typically the boundary between their stellar wind and the interstellar medium....
) of a magnetosphereMagnetosphereA magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the intrinsic magnetic field of a planet or similar body. Earth is surrounded by a magnetosphere, as are the other planets with intrinsic magnetic fields: Mercury, Jupiter,...
. The name "bow shock" comes from the example of a bow waveBow waveA bow wave is the wave that forms at the bow of a ship when it moves through the water. As the bow wave spreads out, it defines the outer limits of a ship's wake. A large bow wave slows the ship down, poses a risk to smaller boats, and in a harbor can cause damage to shore facilities and moored ships...
, 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 ocean surface waveOcean surface waveIn fluid dynamics, wind waves or, more precisely, wind-generated waves are surface waves that occur on the free surface of oceans, seas, lakes, rivers, and canals or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Waves in the...
).
Attached shock
- These shocks appear as "attached" to the tip of a sharp body moving at supersonic speeds.
- Examples: Supersonic wedges and cones with small apex angles
- 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 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 degrees to the oncoming flow (Normal shock), is associated with a Mach number of one. These follow the "weak-shock" solutions of the analytic equations.
Recompression shock
- These shocks appear when the flow over a transonic body is decelerated to subsonic speeds.
- Examples: Transonic wings, turbines
- 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 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.
Shock in a pipe flow
- This shock appears when supersonic flow in a pipe is decelerated.
- Examples: Supersonic ramjetRamjetA ramjet, sometimes referred to as a stovepipe jet, or an athodyd, is a form of airbreathing jet engine using the engine's forward motion to compress incoming air, without a rotary compressor. Ramjets cannot produce thrust at zero airspeed and thus cannot move an aircraft from a standstill...
, scramjetScramjetA scramjet is a variant of a ramjet airbreathing jet engine in which combustion takes place in supersonic airflow...
, needle valve - 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 (oblique shocks) or subsonic (a normal shock) (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.
Shock waves in rapid granular flows
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 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 supercritical 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. Such study is important in estimating impact pressures exerted by avalanches and granular flows on defense structures or infrastructure along the channel and in the run-out zones, and to study the complex flow dynamics around the obstacles and in depositions when the mass comes suddenly to a standstill.Shock waves in astrophysics
Astrophysical environments feature many different types of shock waves. Some common examples are supernovaSupernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
e shock waves or blast waves traveling through the interstellar medium, the bow shock
Bow shock
A bow shock is the area between a magnetosphere and an ambient medium. For stars, this is typically the boundary between their stellar wind and the interstellar medium....
caused by the Earth's magnetic field colliding with the solar wind
Solar wind
The solar wind is a stream of charged particles ejected from the upper atmosphere of the Sun. It mostly consists of electrons and protons with energies usually between 1.5 and 10 keV. The stream of particles varies in temperature and speed over time...
and shock waves caused by galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
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 pulsars.
See also
- Atmospheric focusingAtmospheric focusingAtmospheric focusing is a phenomenon occurring when a large shock wave is produced in the atmosphere, as in a nuclear explosion or large extraterrestrial object impact. The shock wave is refracted horizontally by density variations in the atmosphere so that it can have impacts in localized areas...
- Atmospheric reentryAtmospheric reentryAtmospheric entry is the movement of human-made or natural objects as they enter the atmosphere of a celestial body from outer space—in the case of Earth from an altitude above the Kármán Line,...
- Čerenkov radiation
- ExplosionExplosionAn explosion is a rapid increase in volume and release of energy in an extreme manner, usually with the generation of high temperatures and the release of gases. An explosion creates a shock wave. If the shock wave is a supersonic detonation, then the source of the blast is called a "high explosive"...
- Hydraulic jumpHydraulic jumpA hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface...
- Mach waveMach waveIn fluid dynamics, a Mach wave is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. These weak waves can combine in supersonic flow to become a shock wave if sufficient Mach waves are present at any location. Such a shock wave is...
- MagnetopauseMagnetopauseThe magnetopause is the abrupt boundary between a magnetosphere and the surrounding plasma. For planetary science, the magnetopause is the boundary between the planet’s magnetic field and the solar wind. The location of the magnetopause is determined by the balance between the pressure of the...
- Moreton waveMoreton waveA Moreton wave is the chromospheric signature of a large-scale solar coronal shock wave. Described as a kind of solar 'tsunami', they are generated by solar flares. They are named for American astronomer Gail Moreton, an observer at the Lockheed Solar Observatory in Burbank who spotted them in 1959...
- Normal shock tablesNormal shock tablesThe Normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a normal shock wave. With a given upstream Mach number, the post-shock Mach number can be calculated along with the pressure, density, temperature, and stagnation pressure ratios...
- Prandtl–Meyer expansion fan
- Shocks and Discontinuities (MHD)
- Shock (mechanics)Shock (mechanics)A mechanical or physical shock is a sudden acceleration or deceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation....
- Sonic boomSonic boomA sonic boom is the sound associated with the shock waves created by an object traveling through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion...
- Three-phase traffic theory
- Supercritical airfoilSupercritical airfoilA supercritical airfoil is an airfoil designed, primarily, to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered aft section, and greater leading edge radius compared with traditional airfoil shapes...
- Undercompressive shock waveUndercompressive shock waveAn undercompressive shock wave is a shock wave that does not fulfill the Peter Lax conditions.-Details:Ordinary shock waves are compressive, that is, they fulfill the Peter Lax conditions: the characteristic speed behind the shock is greater than the speed of the shock, which is greater than the...
- Shock diamondShock diamondShock diamonds are a formation of stationary wave patterns that appears in the supersonic exhaust plume of an aerospace propulsion system, such as a supersonic jet engine, rocket, ramjet, or scramjet, when it is operated in an atmosphere...
External links
- NASA Glenn Research Center information on:
- Selkirk college: Aviation intranet: High speed (supersonic) flight
- Fundamentals of compressible flow, 2007
- KB Free finite-element educational software to simulate shocks and detonations.