The park was close to City Airport.
I'm assuming that the aircraft you were watching were approaching to land at City Airport, rather than passing at high altitude.
You were right about the vortices. They are generated primarily at the wing tips, and at the edges of the flaps.
If a vortex is powerful enough, it will lower the pressure at it's centre to a point where any moisture in the air will temporarily condense into water droplets, and cause the 'white trail' to appear.
The presence, or otherwise, of the white trail will depend on the humidity of the air, and the strength of the vortices.
The reason that the trails are there some days and not others, is that some days are more humid.
The reason that, on humid days, some produce trails and some don't, is that some produce more powerful vortices than others.
MJ
Ps.
Mustn't mention the Che****l word....
STB. Quite right. This is no place for that kind of silliness.