http://www.sportskeeda.com/f1/wingtip-vortices-in-formula-one-why-are-they-formed
All quoted from above...
Now let us understand the thermodynamic reason behind the visibility of this interesting phenomenon. The basic assumption is that the whole process is an adiabatic process, with no heat exchange of the system with the atmosphere. So, according to the thermodynamic equation governing the adiabatic process, with an increase in pressure, temperature increases, and with a decrease in pressure, temperature decreases. The temperature we are talking about here is the temperature inside the vortex.
Another temperature which we need to understand is the Dew Point – the transition temperature from gas to liquid, corresponding to partial pressure of water vapour – which determines when we will see the vortices trail and when we won’t. The Dew Point decreases with decrease in pressure, and increases with increase in pressure.
After the formation of the vortex, the pressure inside it decreases significantly as compared to the ambient pressure. This results in a significant drop in dew point (which was already below the ambient temperature before the formation of the vortex) but along with it, there is an even greater drop in the vertex core temperature, which transforms the water vapour into water droplets and hence we are able to see the vortices trail coming out of the rear endplates.
This phenomenon is more prominent in damp conditions because the relative humidity of atmospheric air is high. As more relative humidity means an increase in partial pressure of water vapour, therefore there is a rise in the local dew point inside the vortex. As there is no change in total pressure and temperature, therefore the vertex core temperature now is easily below the dew point, and hence the water vapour condenses.