where T is the total, or stagnation temperature of the rotating gas at radial position r → → , the absolute gas velocity as observed from the stationary frame of reference is denoted with v → → ; the angular velocity of the system is ω ω → → and c p is the isobaric heat capacity of the gas. This equation was published in 2012; it explains the fundamental operating principle of vortex tubes (Here's a video with animated demonstration of how this works). The search for this explanation began in 1933 when the vortex tube was discovered and continued for more than 80 years.