Instability and acoustic fields of the Rankine vortex as seen from long-term calculations with the tenth-order multioperators-based scheme

The instability of the compressible Rankine vortex is investigated using a multioperators-based scheme with the tenth-order approximation to the convection terms of the fluid dynamics equations supplied by the ninth-order dissipation mechanism. The scheme was optimized for high resolution of small scales by choosing its free parameters. The results of long-term calculations with several meshes allowed to reproduce the general scenario of the instability development with self-excitations of different modes and the final stage of rotating quadrupole sound radiation. The calculated frequencies and sound pressure levels are presented for several Mach numbers.