Is there any backward current around a speeding car? If a car (ignoring exhaust, or assuming the engine is off so it is just coasting)
drives past me (standing in the still air's frame of reference), is it possible
for any still spec of dust to deflect backwards because of the generated air flow?
What if the "car" were simply a (non-rotating) sphere?
It seems to me that a funnel could do this (moving with the wide hole in the
front and the narrow hole in the back), so I'm more curious about solids with
no holes and no ground effects.  What shapes then cause the highest "backward air
velocity"?
EDIT:  I think it's easy to see (from answers and analytical solutions I've
found on the internet) that there is instantaneous "backward air velocity"
with about the same magnitude as the "forward projectile velocity", but are
there shapes which can achieve, for example, a 10x magnifier?  I gave the
funnel example, but have no idea of its magnification...hoping
some experts here have looked into this and other shapes.
 A: Think what happens if the car moves forward a small distance. The "slice" of air just in front of the car moves out of the way somewhere, to make room for the car, and an equal sized "slice" of air ends up filling the space behind the car.
So when the car is moving forward continuously, the air near it moves approximately one car-length backwards. Any dust particles in the air will (on average) be moved backwards along with the air.
It makes no difference what shape the car is, so long as the air flow doesn't pass through the car but has to go round it. A cube or a sphere would show the same effect.
A funnel would show a smaller effect. The extreme case would be a "funnel" with no taper, i.e. a piece of pipe. In that case, the air "inside" the pipe would not be disturbed much as the pipe moves forward "around" it.
A: My understanding of this question is, "as reckoned from the frame of reference of the (nearly stationary) air, is it possible for any air movement to take place in the direction opposite to the movement of the car?" Since the car is moving at constant velocity, we can examine this same situation as reckoned from the frame of reference of the car (rather than the air), with no loss of generality.  In this car frame of reference, the bulk air in the far field is moving toward the car (like in a wind tunnel) and the car is stationary.  There is no difference in the dynamics of these two situations.  In the car frame of reference, our question translates to, "relative to the backwards far field constant air velocity, is there any air moving backwards at a greater velocity than the constant far field velocity?  The answer is, of course, yes, because, in the vicinity of the car, the streamlines have to get closer together when they travel around the car.  So, yes, there is a backward current around a speeding car, but only in close proximity to the car.
