Any explosion large enough will make one. It’s essentially a consequence of buoyancy.
The superheated air and smoke from the explosion will rise and form the “cap” of the mushroom. There’s also air flow and heat transfer physics that govern the shape of the cloud, bc the center is hotter than the outer parts, but that’s a little beyond eli5.
Anyway, as the cap rises, air will rush in to fill the void behind it. This pushes all the smoke and dust kicked up from the ground towards the center, which rises because it’s also hot, forming a relatively narrow column of smoke. This forms the stem of the mushroom. There’s also some aerosols that cool off and are no longer lighter than air precipitating out of the cap that makes up the stem as well.
Explosion is just very rapid expansion of air when it gets super hot. Nuke boom makes air hot, it expands, then cold air rushes back in and displaces the hot air that gets pushed up.
It’s not because it’s nukes, it’s just how very large explosions work. A conventional large explosion will have same effect. Nukes are just more powerful, so the effect more pronounced.
The part everyone else is leaving off is why the top mushrooms out. Simply put, it cools off and starts to sink back down, but it can’t sink straight down because of the column of hot air coming up. So it gets pushed out to the sides and then sinks. This results in the column of hot in the middle with a bulb of cooler expanded around the top giving it that mushroom shape.
When the bomb goes off, the air immediately around the blast becomes superheated and rises rapidly (as all hot gases do). Normally, the fireball would be spherical, but that fast-moving upward air causes a vacuum underneath, which causes cooler air on the ground to rush inward to fill the void. The result is that the fireball at the base is being blown inwards while the fireball at the top is still rising outward. Hence the mushroom shape.
Hot air rises.
Air that’s hotter than other hot air will rise faster.
As the mushroom cloud rises, it cools down, meaning the top is moving slower than the air below it. As the faster hotter air pushes past the cooler air, it causes it to swirl, creating that iconic mushroom shape. [Any explosion that is large enough will do this](https://youtu.be/Riauw5UTnW8?si=sduqUMqk-nEoHxIW).
Any large explosive kicks particulate matter into the air. Since hot air rises it’ll form a column but the higher it goes the cooler it gets so as the stuff in the cloud gets higher it’ll start falling away from the middle and back towards the ground but the middle column is still pushing up so it makes a mushroom shape
It’s really just the size of the explosion and the dust. The heat causes the air to rise. The rising dust will spread out, and since it’s heavier than air, start to fall. The falling dust gets sucked into that column of rising hot air, and there you go; mushroom.
With smaller explosions, the force of the blast spreads everything around and doesn’t heat stuff up in the same way for that rising air-column-effect, or at least not enough to raise all that dust/debris with it.
Nukes create an enormous amount of heat. Most other bombs don’t create enough heat to “stick around” – they make a shockwave, they kick up a debris cloud. But much less heat, which just dissipates or blows away in the wind.
The mushroom cloud is not the shape of the nuclear explosion itself – which is a circular shockwave. The mushroom cloud forms later from the leftover heat, like smoke from a giant bonfire. The “stalk” is the hot air rising, compressed into a column by cooler air rushing in. The expanding “cap” is the smoke that reached its max altitude, where it hangs and expands outward. Put them together and you have that weird, foreboding mushroom shape.
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