Criticality of compressible rotating flows

The effect of compressibility on the criticality of swirling subsonic flows is investigated. This study extends previous works by Rusak and Lee [J. Fluid Mech. 461, 301 (2002); 501, 25 (2004)] on the critical swirl of subsonic vortex flows in a circular straight pipe. We derive an asymptotic solution in the case of an isothermal plug-flow with solid-body rotation. In the limit of low Mach number M-0 < 1, it is shown that the critical swirl increases with M-0 as S-c similar to S-c,S-0/(1-M-0(2))(1/2), where S-c,S-0 is the critical swirl of the incompressible flow. This result still holds when varying the thermodynamic properties of the flow or when considering different vortex models as the Batchelor vortex. Physically, compressibility is found to slow down phase and group velocities of axisymmetric Kelvin waves, thus decreasing the rotation contribution to flow criticality. It is shown that compressibility damps the stretching mechanism which contributes to the wave propagation in the incompressible limit.