Why does fire appear to have a defined edge and not simply dissolve out?
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Why **would** it “simply dissolve out”?
Flames have varying appearances depending on a lot of factors. For a really cool extreme example, the Space Shuttle main engines and solid rocket boosters had very different appearing plumes. The solids were bright orange and the three main engines were much less visible: https://commons.wikimedia.org/wiki/File:Shuttle_profiles.jpg This is largely because of the composition of the fuel and oxidizer involved. For the main engines, liquid hydrogen and liquid oxygen burn to form water vapor. For the solids, aluminum powder and ammonium perchlorate. Lots of hot solid particles in the exhaust.
The orange glow of that and of a [Bunsen Burner](https://commons.wikimedia.org/wiki/File:Bunsen_burner_flame_types.jpg) is due to soot particles glowing hot. This is called a [luminous flame](https://en.wikipedia.org/wiki/Luminous_flame). As the particles glow, they cool off and become less visible. Perhaps this is what you’re perceiving as a defined edge?
Note though the different appearances of the flame by opening the air vent allowing the fuel and air to mix before igniting. The more complete combustion gives a different appearance.
Fire science actually gets pretty complicated so I’m not sure which part to simplify to try to answer your question.
Anyway, check this video where Veritasium takes a fire into simulated zero-G: https://youtu.be/xdJwG_9kF8s
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