Physics/chemistry behind the observation
This is purely observation based. Any time I have cooking something on the stove, if I change intensity in any direction - reducing or increasing the heat, it seems like water vapor threads shoot out from the pot.
I can understand if I increase the heat, more energy, but don't have any explanation for reducing the heat. It seems like state change any direction causes some water vapor to release.
Don't think it matters, but it's gas based stove.
What causes the vapor or threads of mist to shootout when there is a change ?
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I don't know about turning the heat up and your observation, but seeing more "steam" when turning the heat down or off is often wondered about. It was asked and answered on the physics stack exchange. Basically, since "steam" is transparent water vapor, what you are seeing when the cooling happens is a cloud of condensed water vapor. The issue with the observation and answering the questions lies in the difference between true steam and this condensate. There is more information in the link. What you are seeing when you turn the heat off (or down) is the condensation of the water vapor, which obviously happens at a lower temperature than that needed to keep the water vapor transparent (at least most of it...which is way you always see a little of the condensate).
By the way, it looks like there is a duplicate question in physics, as pointed out in the comments above.
I think what you're observing has a common name in the culinary world. It's called carry-over heat. Assuming you have a big pot on the stove, and the heat source is at the bottom. The bottom of the pot is hotter than the top of the pot; say there's a 5C difference. Bottom is 99C, top is 94C (almost boiling)
Even when you turn off the heat, the heat from the bottom portion of the liquid will continue heating the top portion to an equilibrium between 94 and 99. Say 96; and 96 is already good enough to observe steam on the top.
It's hard to say without seeing it, but I suggest that this phenomenon happening when you turn up or down the gas may be caused by your arm reaching out in the vicinity of the pot to turn the knob.
The air above the pot should be saturated with water vapor at a higher temperature. Motion nearby will create eddy currents that carry that moist air to where it can meet cooler air. You see the moisture when it condenses to fog.
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