Many, often contradictory, explanations for the vortex tube effect have been advanced over the years since its invention/discovery. Analysis of the various suggestions reveals only two firm facts
(1) As of 1996, no-one knows for sure the details of how the energy separation in the vortex tube arises. A number of authors have written confidently about their theories, but all have serious difficiencies or are called into question by subsequent experiments. I advance a summary of my best guess below, based on experiments, simulations and analysis but I would not for a moment suggest that it represents a definitive explanation
(2) The vortex tube is a tough nut to crack. The energy/temperature separation is a complex and subtle phenomenon. Anyone who solves the mystery definitively will do so as the result of a serious programme of experimental and theoretical research. While qualitative. back of the envelope type explanations may be useful to get a basic handle on what is going on, there is no way they can do more than scratch the surface.
The next major step in understanding of the vortex tube will be for someone to advance a predictive theory that can be used, either computationally or analytically to predict the performance of real vortex tubes.
Present CFD codes can do a reasonable job of estimating the flow pattern through vortex tubes, but make a complete hash of estimating the energy separation.
My results suggest that energy separation in the Ranque-Hilsch tube can be accounted for by two phenomena. Firstly, the formation of an approximately forced vortex near the tangential inlets to the tube initially provides a kinetic energy separation, the peripheral gas having a much higher velocity than that near the centre. Secondly the strong radial pressure gradient produced by the forced vortex enables turbulent fluctuations to transport thermal energy radially outwards and re-enforce the existing energy separation until the thermal and pressure gradients have come into equilibrium
The effects of the two processes are modified by axial convection and by viscous dissipation of the kinetic energy of the flow to produce the characteristic distributions found within the vortex tube. Axial cnvection extends the turbulent thermal transport process over a significant length of the tube, and is responsible for the observed axial development of the energy separation. Viscous dissipation converts the kinetic energy separation into a thermal separation, and serves to produce a temperature rise in both the hot and cold streams as their kinetc energy is reduced.
The energy separation is maintained by the flow so long as the swirl is strong enough to provide a substantial radial pressure gradient to help offset the effects of turbulent conduction. As the swirl decays, for example towards the end of a uniflow tube, the energy separation declines.
Such an explanation is consistent with many observed features of vortex tubes, essentially attributing the existance of a radial stagnation enthalpy gradient to the formation of a forced vortex, and the cooling of the central flow below the inlet temperature to a turbulent transport process that depends on the compressibility of the fluid. In particular it would explain why a vortex tube operated on high pressure water produces an energy separation, but with no net cooling of the central flow (Balmer).