You write about what you do, but not how you do it. Lowering the pitch via the embouchure is obvious. You relax the muscles and/or lower the jaw. What are the "mechanics" of lowering the pitch using the airstream? Does it involve changing the shape or size of the opening inside the mouth? Is it related to the speed of the airstream? What role does the back of the tongue play, if any?
This is a fascinating subject. Can you give some more specifics about how you do this? Thanks.
It has everything to do with the back of the tongue. The muscle movements that take place in your vocal tract which affect pitch and timbre are subtle and complex, but your vocal chord position and back of the tongue definitely both play a role. Air speed remains generally constant or sometimes even increases.
A simple way to begin experimenting with this is trying to do a pitch bend down using the back of the tongue. Keep your jaw and embouchure stead, and experiment with lowering the back part of your tongue.
If your interested in an in depth practical study the book mentioned in my forum signature is all about the mechanics of the vocal tract and embouchure. It covers this subject from it's basic beginning and takes it through to an advanced level of mastery.