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>That's almost twice the speed of sound.

a bit of pedantism - giving that it was air heated by the radiation and shock wave the speed of sound was much higher, so while going up very fast, the dirt being moved up by convection and pressure differential may have still moved subsonically wrt. the local speed of sound.

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I put the speed of sound purely as a comparison. The local speed of sound is irrelevant because the dust was moving with the medium and not relative to the medium.

Except for the situation of being directly impacted by shockwave, the medium - air in this case - can't move faster than the speed of sound, ie the speed with which the pressure differential causing the movement is propagated. Once the fireball expanded and shockwave passed, the mushroom goes up because it's hot and thus it is moved by the atmospheric pressure. For example you wouldn't have mushroom going up without an atmosphere. It is able to go that fast because the whole surrounding volume was preheated by radiation and the shockwave with the resulting speed of sound increase .

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