Cyclostrophic adjustment in swirling gas flows and the Ranque-Hilsch vortex tube effect

A theoretical analysis of cyclostrophic adjustment is presented; i.e., adjustment to balance between pressure gradient and centrifugal force in axisymmetric flow of an inviscid gas is examined. The solution to the problem is represented as the sum of a time-independent (balanced) and time-dependent (wave) components. It is shown that the wave component of the flow in an unbounded domain decays with time, and the corresponding solution reduces to the balanced component. In a bounded domain, the balanced flow component exists against the background of undamped acoustic waves. It is found that the balanced flow is thermally stratified at Mach numbers close to unity, with a substantial decrease in gas temperature (to between ?50 and ?100°C) in the axial region. This finding, combined with the results of special experiments, is used to explain the Ranque-Hilsch vortex tube effect.