Is cigarette smoke an example of turbulent flow? Everywhere in internet and books that introduce to fluid dynamics mention cigarette smoke as a classical example of turbulent flow.
But the velocity, in other words the Reynolds number, is small. How could be that this flow is turbulent?
 A: 
The meaning of the Reynolds number is that the equations of viscous fluid flow allow similarity: if the geometry is matched (up to a scaling factor) between two setups, and the Reynolds numbers are matched, then the equations describing fluid motion are the same in normalized variables, which means that the character of motion (laminar or turbulent) should be matched as well. This follows from an algebraic transformation of the equations, and there is nothing there that would predict that motion has to become turbulent for $Re$ above a particular value, e.g., $Re$ = 1. On the other hand, the physical interpretation of $Re$ as the ratio of inertia to dissipation implies that increasing $Re$ should eventually lead to a transition to turbulence. However the numerical value of critical $Re$ depends on the geometry. In some standard cases, e.g., flow in round pipes, it is known that transition to turbulence happens at $Re$~1000; but this does not say that in a different setup a value as small as $Re$~10, in case of a cigarette, would not be enough to make the flow turbulent. So whether in a particular setup the Reynolds number is sufficient for transition to turbulence is up to an experiment (or a detailed simulation). For a cigarette, experimental results, e.g., in the picture, clearly demonstrate that initially laminar rise of hot air plume from a cigarette transitions to disordered, turbulent, motion of air a few cm away from the tip of the cigarette.
Below are a couple of insightful videos showing turbulent plumes from a candle 
https://www.youtube.com/watch?v=mLp_rSBzteI
and from a match https://www.youtube.com/watch?v=TQJAokQQbmI
A: First of all, cigarette smoke is cigarette smoke; it's not an example, it's not a flow, and it's not turbulence. People need to keep concepts and categories straight in their heads, otherwise nothing but complete and utter confusion arises.
Now, if you are asking whether the thermal convection flow that is induced by the heat from a cigarette in still air and that is made visible by the smoke particles from the cigarette is an instance of turbulent flow, then the answer is no. The Reynolds number in this case is indeed too low for turbulence to develop, and detailed measurements of the velocity field will clearly demonstrate that the flow is fully laminar. No responsible and even halfway competent textbook would mention this flow as an example of turbulent flow.
