Snowbird writes:

Now, the induced drag is
creating the tip vortices, which presumably descend, but parasite drag has
no vertical component, so in theory it should stay in place. So according to
this, the higher the airplane's relative speed, the slower the wake will
descend (if at all).

The entire air mass behind the aircraft is descending. The downwash descends,
and air from above moves down to replace it. While parasitic drag is not
associated with lift and thus has no vertical component of its own, any
turbulence it creates will still drift downward with the downwash, although
perhaps less quickly than the downwash itself, depending on where the
turbulence leaves the aircraft.

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