All those old comments are great and valid I think, but here's another tip if anyone's interested (and I'm interested in seeing if anyone else can concur).
I find that I can do it on demand (with concentration) by opening my mouth wider to get this tone - that is, leaving the embouchure on the mouthpiece the same, just increasing the distance between my top and bottom teeth. Sometimes I even jut my jaw out a little to get it even more.
Then the fleshy lip parts just "flap in the breeze" so to speak and the real tone goes away proportionally and the airy-ness increases.
It's weird. Also, I can do it MUCH more effectively with my Bach 3C mouthpiece than anything else like my Curry TF which is a deep V (flugel-ish) mouthpiece. Maybe the Curry is already "filtering" out the high frequencies and the 3C is not, and it's actually the high frequencies that are the "air" sound.
For me, it takes some concentration to initially get it going (this is getting faster as I practice it), but I can "snap" out of it instantly and get my normal tone back for some cutting tones. Fun.