Unless I am mistaken:It seems that many of the snake oil salesmen want us to believe their Klangbogen or dense metal lyre screw affects and enhances air flow inside the instrument. The reality is there is very little air flow in a woodwind instrument. The air is essentially sitting there inside the instrument and the molecules that make up the air are set to vibrating by the reed. When you blow into a sax or any other woodwind you don't really blow much air. It's just enough to make the reed vibrate and probably not enough to make a strip of paper, or a feather, move if laid across the end of a sax, clarinet, flute or bassoon. I'm sure if you used sensitive enough instruments you could measure the volume of air moving through the instrument over a given period of time but the flowing air is not what is making sound. It's the vibrating air molecules knocking up against each other, transmitting energy from one to the next, and causing a wave to spread out like ripples on the surface of a pond.
We can talk about AC and DC electricity.
In exactly the same way, we can talk about air flow.
Sure, the "DC" air flow through a sax is small.
However the air inside the sax oscillates... fast. (And with increasing amplitude as we get to pressure antinodes, eg openings to the air column.)
That oscillation is air dashing up and down the air column, or in and out of a tone hole.
It might be laminar in its oscillatory flow, or turbulent. There is a lot going on... It could be seen as "AC" airflow.
Relative to a fixed spot in the bore, the air is dashing up then down, alternating very fast. It therefore encounters boundary effects (friction) against the walls that contain it. Turbulence is introduced where it encounters interruptions to the bore.
It changes direction to oscillate in and out of a tone hole. (And it is that oscillation in and out of a tone hole that is the initiation of the travelling wave that gets to the listener's ears.)
So it is rather misleading to say that there is negligible airflow. The "AC" air flow is very real and fast. It is responsible for making the sound.
That "AC" oscillation is different from "vibration of the air molecules". That vibration is at a molecular level and is what is responsible for heat/temperature.
While the molecules are vibrating, they travel one way then back, fast, repeatedly. That is the "AC" airflow I write about, that makes the sound.