Shock Waves
A shock wave is essentially a surface of discontinuity propagating supersonically through a medium. Density, pressure, and temperature are unequal on the different sides of the wave front, clearly distinguishing between the shocked and unshocked material. This is in sharp contrast to subsonic sound waves, where all thermodynamic quantities vary continuously through the medium. In general, the shock compresses and heats the material that it flows through in an irreversible process, again in contrast to sound waves. The fact that the front propagates supersonically with respect to the unshocked material allows for the discontinuity to be maintained as the wave advances, since it impedes information from being transmitted from the region through which the shock has already passed.
Shock waves generally accompany supersonic motion, such as a sonic boom or the impact of projectile on a surface (like a meteor hitting the earth). Shock waves are especially associated with events where a large amount of energy is deposited in a small volume--an explosion. A special kind of shock wave-induced explosion is a detonation, where energy deposited by the shock is sufficient to drive an exothermic reaction in the material it passes through, as with a gasoline tank or TNT. Shocks are generally transient phenomena: without a constant supply of energy, pressure in the material behind the shock will gradually decrease as its volume increases, until the propagation speed becomes subsonic and the perturbation reduces to a sound wave.
The basic physics of shock waves is usually described by the textbook example of an infinite tube of gas held at one end by a piston at rest. If the piston is accelerated instantaneously to a supersonic speed into the gas, the solution of the flow is a propagating front, where the (shocked) gas behind it settles at uniform density and pressure that are both higher than the unperturbed gas before the front. The properties of the gas on both sides of the discontinuity can be related through the general equations of conservation of mass, momentum, and energy across the front, known as the Rankine-Hugoniot equations. It can also be shown that the flow settles on a self-similar form, meaning that the spatial profile of all quantities in the flow remains constant in time up to a scale, which is the only time-dependent function. Such self-similar behavior is typical of strong shocks.
There exist several sub-classifications of shock waves, according to specific properties. Shocks where the direction of propagation is not normal to the shock front are called oblique shocks, and offer a wide variety of reflection and diffraction phenomena. A weak shock, where the pressure in the unshocked material is not negligible with respect to the pressure in the shocked region, also introduces interesting variations with respect to the simpler case of a strong shock. In astrophysics, there is great interest in radiative shocks, in which energy can be emitted from the shocked region beyond the shock front, (the textbook case, where no energy can overtake the shock front is called an adiabatic shock).
The origin of shock wave theory can be traced back to B. Riemann's work on the propagation of acoustic disturbances and the experimental study of supersonic flow by E. Mach, both in the second half of the nineteenth century. However, theoretical and experimental investigation of shock phenomena has emerged in earnest as part of the atomic bomb project in both the United States and the Soviet Union. The study of shock waves has since become a fundamental aspect of fluid dynamics and plasma physics, as well as astrophysics, where shocks are very abundant (and also tend to give rise to excessive emission of radiation, and hence become observable, even at large distances). Theoretical and experimental studies also concern the response of different types of materials to shock loading and instabilities that arise due to passage of a shock between different materials (Rayleigh-Taylor and Richtmayer-Meshkov instabilities). Physics of the shock front is another subject of interest: the discontinuity is never really infinitely thin, and its width is determined by the chemical processes that distribute the energy and entropy which have been deposited. While the width of the front is generally much smaller than any other typical length scale of the flow, its properties are potentially important in determining the stability of shock propagation and the efficiency of detonation fronts.
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