Shock diamonds

Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, donut tails or thrust diamonds) are a formation of standing wave patterns that appear 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 abrupt changes in local density and pressure caused by standing shock waves. Mach diamonds (or disks) are named after Ernst Mach, the physicist who first described them.

Shock diamonds form when the supersonic exhaust from a propelling nozzle is slightly over-expanded, meaning that the static pressure of the gases exiting the nozzle is less than the ambient air pressure. This pressure increase in the exhaust gas stream is adiabatic, and reduction in velocity causes its static temperature to be substantially increased. This causes reignition of the unburned combustion products in the engine’s exhaust. The exhaust is generally over-expanded at low altitudes, where air pressure is higher.

As the flow exits the nozzle, ambient air pressure will compress the flow. The external compression is caused by oblique shock waves inclined at an angle to the flow. The compressed flow is alternately expanded by Prandtl-Meyer expansion fans, and each "diamond" is formed by the pairing of an oblique shock with an expansion fan. 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

...
Wikipedia