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In this video one can see how cigarette smoke changes from laminar to turbulent flow. The conditions, though, are far from ideal (by which I mean that the air in which the smoke flows has no common movement and the quality and quantity of the released smoke do not change in time).

Nevertheless, the video shows clearly that at varying regions the laminar flow shows changes in a turbulent, clearly patterned (laminar-turbulent-laminar-turbulent,etc.) flow.

Now, the onset of turbulence depends on the smoke's Reynolds number, and the higher the velocity of the smoke, the greater this number, so at a certain height (which of course varies with temperature and pressure of the air), the smoke, due to the interaction with the air, turbulence develops.

Does the smoke itself also contributes to the turbulence, or is the turbulence only due to the interaction with air? In other words, if we let the smoke come out of a small pipe in outer space, with varying velocities, but the same qualities (for example, different temperatures in different parts of the smoke), will the smoke develop turbulent behavior, or, so to speak, fall over itself. Or, in still other words, what happens to the Reynolds number? My guess is that no turbulence develops (low Reynolds number), but I'm not sure. Maybe there are internal frictions, though that's hard to imagine if the smoke has a uniform velocity.

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    $\begingroup$ Good question, but sorry don't know the precise answer. The example you illustrate I suppose involves both smoke particles and gas molecule interactions. When you mention 'outer space' you have to be careful in that you are introducing yet another factor that does have an influence on convective flow - gravity. I would expect the absence of gravity to have an even larger effect than the absence of air molecules. $\endgroup$ – docscience Nov 27 '17 at 15:52
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    $\begingroup$ I'll further add that in a gravitational field the direction of convective flow opposes gravity. In space without gravity, differences in radiation or conduction of heat to surrounding still gas field (if present) will be the only forces directing smoke particle motion besides collision forces of the smoke and molecules themselves that drive diffusion (Brownian motion). $\endgroup$ – docscience Nov 27 '17 at 15:59
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    $\begingroup$ Do you have a way to produce smoke without it being mixed with the oxygen source that fuels the combustion producing the smoke? If you just somehow throw ash particles into a vacuum, I think you've got a bunch of ballistic ash particles, not "smoke". $\endgroup$ – The Photon Nov 27 '17 at 16:57
  • $\begingroup$ -1 Not clear what you are asking. If leaked into a vacuum, isn't the smoke just going to disperse very quickly? How will convection happen in this scenario? Why do you think the smoke is going to show fluid properties? $\endgroup$ – sammy gerbil Nov 27 '17 at 18:53
  • $\begingroup$ @The Photon-The cigarette smoke is produced in a chamber full of tobacco and oxygen, after which it's blown through a small pipe (ignoring the smoke's interaction with the pipe) which in my opinion is ordinary cigarette smoke. $\endgroup$ – descheleschilder Nov 27 '17 at 20:03
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First off, whenever fluid inertia becomes substantial compared to viscous forces, instabilities of the flow are amplified and the flow becomes turbulent. Reynolds number is a measure of the competition between inertia of the fluid and viscous forces acting on it. See that the mechanism by which inertia of the flow is increased in comparison to viscous forces is irrelevant. In convection (where gravity must necessarily be present) increasing temperature difference is one way to increase inertia of the fluid relative to viscous forces (what really matters is the magnitude of Rayleigh/Grashof number).

Now if you go to outer space where there is no gravity, then there cannot be flow due to convection. However there are other ways you can create a flow, for example by imposing pressure gradient or by imposing surface tension gradients (see Marangoni flows). Therefore there are other means by which you may control inertia of flow relative to viscous forces. Again once inertia of flow becomes substantial compared to viscous forces turbulence will ensue (assuming that viscous force is the only retarding force).

So to answer you question, it is true that surrounding air plays a role in making the cigarette smoke turbulent; after all it is the temperature difference between surrounding air and smoke that drives the motion. However presence of air is not necessary for smoke to become turbulent, provided you find some means creating the flow in the first place. Look at the rocket exhaust in upper atmosphere where there is hardly any air, or coronal mass ejections from the sun.

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