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I observed that when a mosquito coil is lit and kept on the floor then the smoke raises almost linearly but after some distance covered vertically, their path of motion gets completely distorted. It is to be noted that there were no means of wind or something in my room as the windows/doors were closed and electric fans/AC were turned off. So why does that happen? I also noticed that for no reason the smoke was losing its linearity from the beginning sometimes.

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The smoke particles are tracers of air movement- in this case, the air which rises because it was warmed up slightly by the burning coil. The air rises very slowly which means there's not much energy loss from viscosity and this means that small perturbations in its travel will persist, rather than being damped out. So those perturbations (the "swirling" patterns) will accumulate and add to one another.

This means that tiny perturbations right at the at the start of the rising air column get magnified, and after a while those perturbations grow so big that the column is disrupted in ways that are extremely complex and changing from moment to moment. This makes the system behavior very hard to predict after a while- and the smooth predictable rise of the air column switches into random, misshapen vortices.

The growth of those vortices is an extremely complex phenomenon that got its first mathematical treatment by a guy named Von Karman in the late 1940's.

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