What causes the formation of beads in rocket exhaust plumes?

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The formation of beads in rocket exhaust plumes, often referred to as "shock diamonds," is primarily influenced by the physics of fluid dynamics and the nozzle shape. These beads appear at regular intervals and are more pronounced with higher thrust levels. The phenomenon occurs due to pressure changes and shock waves in the exhaust flow, which create distinct patterns in the plume. Factors such as temperature and luminosity may also play a role in their visibility. Understanding these dynamics is crucial for optimizing rocket performance and exhaust characteristics.
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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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