I call them by their proper name, medusae.
I think I have a picture of that species, which I found just in front of my house,
on my seashore CD under the heading Cnidaria - look it up.
When I was an undergraduate I found the Cnidaria
(then called Coelenterates) fascinating, and they were always washing up
on the beaches around Liverpool, especially after storms.
I learned them really well for the exams.
We have a common medusa here called the Lion's Mane,
which has a nasty sting.
The common freshwater Hydra you see in High School Biology courses
is an example of the polyp half of a cnidarian life sycle
(its tentacles stick up rather than down, but it has the same kind of
stinging cells).
Corals are also Cnidaria, just the polyp part of the cycle
