We already know that the current F1 car deals badly with turbulence so let us have a look at where it comes from. Well, primarily, it is caused by a car disturbing the air as it passes through. The shape and speed of the car determines the severity of the turbulence. A F1 car creates huge turbulence because of its speed and shape. Wings certainly leave a lot of turbulence behind but the diffuser does its fair share too, and that is close to the ground where a following car's front wing is severely affected.
Wheels also create a lot of turbulence.
We have all experienced the effect of turbulence behind large vehicles on an expressway. Regardless of the shape most of the turbulence is created by the flow to fill the hole the vehicle punches through the air. The severity of the turbulence increases dramatically as the speed of the vehicle is increased. Another thing to realise is that turbulence doesn't move. Again we do not know how long this is but it seems to be around 10 to 15 car lengths and could be as wide as two cars at its widest.