I think the actual "effect" you're looking for is achieved by closing the throat ... just a bit, and pushing the air from lower in your throat. Wind players (like myself) learn to support the air flow with a contraction of our diaphragm muscle. It's hard to explain, but think of the feeling you get in your lower abdomen when you're constipated, and trying to push out ... well, you know.💩(sorry, not trying to be gross)
When done correctly, using supported air, and not just volume, it is not damaging, and can be controlled quite easily.
I've said many times that the best vocal lessons I ever learned were actually techniques from playing woodwind instruments. Clarinet, sax, flute etc ... all gave me valuable breath control, and stamina that I might not have had otherwise.
Try this ... open your mouth (a normal distance) and sing the syllable "Ahhhhh" ... gradually lower the intensity of your air flow, and start to close off your throat. You should hear that "Growl" start to emerge. Experiment with adding different sounds, words etc, and see if you can grasp the concept. How this helps.
BTW:
The sax growl, in a real instrument is actually achieved by rolling the tongue, like a long RRRRRR-type sound. It forces the air to travel quicker, and the reed vibrates in a more unpredictable pattern.
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