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From my point of view, high gas pressure input creates air rotation inside the tube. Due to the rotation, the kinetic energy in the air change to internal energy. The internal energy release as heat energy. The heat energy goes out and the cold air stay. The cold air flows back to the other end to create the cold air flow.
If what I am thinking is right, I don't understand why the inner vortex tube is cold. From the circular motion point of view, air needs more kinetic energy to rotate in a smaller radius than in a larger radius. This could draw a conclusion that the air in the inner tube rotates slower than the air in outer tube.
I read the following from Wikipedia
What is usually agreed upon is that the air in the tube experiences mostly "solid body rotation", which means the rotation rate (angular velocity) of the inner gas is the same as that of the outer gas. This is different from what most consider standard vortex behavior — where inner fluid spins at a higher rate than outer fluid. The (mostly) solid body rotation is probably due to the long length of time during which each parcel of air remains in the vortex — allowing friction between the inner parcels and outer parcels to have a notable effect.
How I understand is difference from Wikipedia. Do I make some conceptual mistake? Please help