As a Caltech alum, I am compelled to point out that Dabiri did 90% of the work on this at his former institution. Way to go Stanford PR team, I'm sure he figured it all out in a year on your dime.
Just from the look of it, it appears something like: take in water through a large aperture, expel it through a small one (which is actually the same one, contracted).
Headline should read: "Jellyfish discover the trick jellyfish use to swim". It amuses me that "scientist discover such-and-such" can be contrasted with the fact that such-and-such worked out how to do it millions of years ago. We think we're so advanced.
