Some special wave solutions in an adiabatic gas in solid-body rotation

Waves occurring in a compressible inviscid fluid rotating as a solid body within a circular cylinder are reexamined for the particular case where the disturbance frequency in the rotating system is equal to twice that of the rotating fluid. It is shown that for this frequency there exists a stable wave provided a certain relationship is satisfied between the harmonic m, the axial wavenumber b, and the peripheral Mach number M of the flow. For γ=1.4, where γ is the ratio of the specific heats of the gas, there are solutions for only the first five harmonics and for γ=1 there are solutions for all harmonics. These results are at variance with the conclusions of Gans [J. Fluid Mech. 62, 657 (1974)] and Kerrebrock [AIAA J. 15, 794 (1977)], who suggested that there are no waves for this configuration.