Fluid dynamics doesn't depend on whether an object moves through a fluid or whether the fluid flows past an object. Aerodynamics refers to moving air, as opposed to hydrodynamics that studies moving water and fluid dynamics that studies any kind of moving fluid. The size and shape of wakes depend on the fluid's viscosity, the relative speed between the fluid and object and the object's shape and size. Viscosity is a measure of a fluid's thickness or resistance to move. Oils are more viscous than water.
Water is more viscous than air.
The air's viscosity changes with altitude. The relative speed between a fluid and an object influences the wake structure. Convected air flow past a burning cigarette is slow speed flow. Air gets heated by the cigarette and rises in a series of random, but distinguishable, curves. When the air flow increases, by moving the cigarette through the air or by blowing across the tip, the flow becomes more and more random.