Hey Bruno, ok...here's a shot...for this post I will stick to the physical stuff, it seems like when I start including too much of the energetic component it isnt coherent enough for the reader. It is substantially easier to do this with natural abdominal breathing especially to start out.
Turbulence is simply something to eliminate. As air moves along a landscape, vortices form amongst the nooks and crannies. The idea is to streamline the mechanisms to the point at which the flow of air is so smooth that it doesnt even trigger a neural response, i.e. you cant feel the air moving.
The way I did this was basically:
-cease using the nose, sinuses, throat, bronchi, lungs to facilitate the movement of air
-harmonize and strip down to just the main physical components: diaphragm, psoas, perineum.
I dont include the front of the abdomen in this context because eventually it drops as "the breath externally disappears" and my own pursuits have revealed that when pursuing longevity breathing. I use this as part of a session most often, to open and close with. Plenty often I will include an active portion of the meditation where I'll do lower dantien breathing or something, but to wrap it up I always revert to this longevity breathing protocol.
Given that this practice tends to develop inertia over time, how much progress you make with it is really dependent on your current level of understanding and practice.
No prerequisites outside of learning to identify the physical structures. This is intended to be a foundational prerequisite for pretty much any energetic practice.
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Ok - so as you first begin working with the idea of not using the sinuses or anything to facilitate breath, the idea with that is to attenuate signals, and the 40 cycle/sec resonance of the olfactory nerve that is produced by normal breathing is a good place to start. The longer term intent is to be able to well attenuate all of the cranial nerves that make up the myriad sensory input we are constantly bombarded with.
Put the energy of your awareness into the timing of the breath mechanisms.
To begin an inhale, descend the diaphragm from its bottom rear attachment point along the anterior spine. The diaphragm actually merges into the anterior longitudinal ligament that runs the length of the spine - the psoas does too. Since the diaphragm physically does not "extend all the way down to the dantien" that is partly why there is that focus on the psoas, since it is joined so long as you keep that intent to keep gently descending for the duration of the inhale, that serves the purpose.
The perineum has a relatively short distance to travel; be gentle, let it softly expand on the inhale and gently lift on the exhale.
If you consider the energy generated by the movement, there is a sort of energetic culmination towards the end of the motion - if you've ever seen a dyno readout from a car's engine you can see the power generated follow a slope upwards and then peak a bit before red line. Same concept here - each physical component can be treated as having its own slope, and working on the timing of breath we want the energetic maxima to be concurrent. (So in doing all of this calmly, you are looking for an energetic maxima amidst a consumption minima.)
In the beginning stages of this, the stomach relaxes on the inhale and gently firms on the exhale, providing some subtle support. As progress is made, the need for that support diminishes and disappears.
Lengthening of the breath, take baby steps. If you try to make too much progress too quickly then the body's failsafe mechanisms feed back and you get increased heart rate, the urge to breathe, etc.
Plenty often I have spoken of ingraining a breath protocol onto the subconscious - you already have one, but what this does is reprogram it to be more efficient. The subconscious processes can be trained, this is a start at it. So once habit-energy is established, the effects carry over to non mindful states, sitting at a desk working...sleeping - my wife told me she can tell when I am in good practice not by how long I am sitting there meditating, but by how my breath is when I sleep!
Another key is to work on smoothing out the transitions between inhales and exhales - that's actually where I came up with the how to begin a breath in the first place...I had slowed everything down to the point that my diaphragm would hiccup because the mechanics were not proper enough...but that really only comes about when you've put the onus of breath on the diaphragm-psoas-perineum dynamic and have let go of the sinuses.
This helps with the issue of awareness gapping - so when you find yourself not paying attention to the breath process, return to it. As often as necessary. Dont fret over it, think about how long you werent paying attention, or anything like that. Just return to the breath. Doing these simple things cultivates a habit energy that carries forth into your subconscious processes.
I will return to effects etc tomorrow, running out of time this evenin...if there is anything you would like me to clarify I can do so then also

If this sounds a bit tedious...well, it is, in a way. It is a very rote method, and the downstream effects are a habit energy that carries forth into daily life, sleep, everything...if one is to "awaken" and find superlative awareness carrying forth into all aspects of one's life, I feel this cultivated habit-energy is a very powerful tool towards that.