What causes the formation of beads in rocket exhaust plumes?

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SUMMARY

The formation of beads in rocket exhaust plumes, often referred to as 'shock diamonds', is primarily influenced by the nozzle shape and the thrust produced during launch. As observed in recent rocket launches, these beads appear at consistent intervals, which correlate with increased thrust. The phenomenon is a result of pressure fluctuations and temperature variations within the exhaust flow, rather than a continuous expansion of the plume. This behavior is also evident in afterburners of jet engines, confirming the underlying physics of shock waves in high-speed exhaust flows.

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Artlav
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Not sure if it's chemistry or physics, but the latter seems more like it.

Let's take a look at pretty much any large rocket with smoke-less exhaust during it's launch, for example the recent one:
427802.jpg


As you can see, there are a kind of beads in the exhaust plume at seemingly constant intervals. The higher the thrust, the longer the intervals.

What causes these beads? I think they are related to the nozzle's shape, but if so, why are there several of them? What prevents it from expanding at where the first bead is, and keep going? Or, does it look this way for some other reason, like temperature/luminosity/etc?
 
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