Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, doughnut tails or thrust diamonds) are a formation of standing 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. The diamonds are formed from a complex flow field and are visible due to the ignition of excess fuel. Mach diamonds (or disks) are named for Ernst Mach, the physicist who first described them.
Shock diamonds form when the supersonic exhaust from a nozzle is slightly over or under-expanded, meaning that the pressure of the gases exiting the nozzle is different from the ambient air pressure. The exhaust is generally over-expanded at low altitudes where air pressure is higher, and under-expanded at higher altitudes.
As the flow exits the nozzle, ambient air pressure will either expand or compress the flow; over-expanded flow is compressed while under-expanded flow expands. The compression or expansion is caused by oblique shock waves inclined at an angle to the flow. When the compressed flow becomes parallel to the center line, a shock wave perpendicular to the flow forms, called a normal shock wave. The first shock diamond is located here and the space between it and the nozzle is called the "zone of silence". The distance from the nozzle to the first shock diamond can be approximated by:
where x is the distance, D0 is the nozzle diameter, P0 is atmospheric pressure and P1 is flow pressure.
As the exhaust passes through the normal shock wave, its temperature increases, igniting excess fuel and causing the glow that makes the shock diamonds visible. The illuminated regions either appear as disks or diamonds, giving them their name.
At each shock diamond, the flow becomes compressed enough that it expands outward in a set of expansion waves called the expansion fan. Eventually the flow expands enough so that its pressure is again below ambient, at which point the expansion fan reflects off the contact discontinuity (the outer edge of the flow). The reflected waves, called the compression fan, cause the flow to compress. If the compression fan is strong enough, another oblique shock wave will form, creating a second shock diamond. The pattern of disks would repeat indefinitely if the gases were ideal and frictionless, however, turbulent shear at the contact discontinuity causes the wave pattern to dissipate with distance.
Alternative sources 
Shock diamonds are most commonly associated with jet and rocket propulsion, but they can form in other systems.
When artillery pieces are fired, gas exits the cannon muzzle at supersonic speeds and produces a series of shock diamonds. The diamonds cause a bright "muzzle flash" which can expose the location of gun emplacements to the enemy. It was found that when the ratio between the flow pressure and atmospheric pressure is close to one, the shock diamonds were greatly minimized. Adding a flare to the end of the muzzle balances the pressures and prevents shock diamonds.
Some volcanoes have been shown to produce jets containing shock diamonds. The ash-gas mixture output by a volcano has a speed of sound on the order of 100 m/s, and many eruptions are known to have exit velocities well in excess. This makes the base of the eruption supersonic, leading to the same dynamics that produce shock diamonds. These highly destructive jets have occurred in gas-rich volcanoes such as Mount St. Helens and Krakatoa.
Radio jets 
Some radio jets, powerful jets of plasma that emanate from quasars and radio galaxies, are observed to have regularly spaced knots of enhanced radio emissions. The jets travel at supersonic speed through a thin "atmosphere" of gas in space, so it is hypothesized that these knots are shock diamonds.
See also 
|Wikimedia Commons has media related to: Shock diamonds|
- Norman, p. 48
- Scott, Jeff (17 April 2005). "Shock Diamonds and Mach Disks". Aerospaceweb.org. Retrieved 6 November 2011.
- Niessen, Wilfried M. A. (1999). Liquid chromatography-mass spectrometry, Volume 79. CRC Press. p. 84. ISBN 978-0-8247-1936-4.
- "Exhaust Gases' Diamond Pattern". Florida International University. 12 March 2004. Retrieved 6 November 2011.
- Norman, p. 41
- Ogden, Darcy E. (2008). Fluid dynamics of high pressure volcanic eruptions. ProQuest. pp. 6–7. ISBN 978-0-549-65624-1. Retrieved 7 November 2011.
- Norman, p. 45
- Norman, p. 68
- Norman, p. 51
- Norman, Michael L.; Winkler, Karl-Heinz A. (Spring/Summer 1985). "Supersonic Jets". LOS ALAMOS SCIENCE. Los Alamos National Lab. Retrieved 6 November 2011.