Viscous and inviscid spatial stability analysis of compressible swirling mixing layers

We examine the viscous and inviscid spatial stabilities of circular swirling mixing layers that differ in swirl intensity, Mach number, and Reynolds number. The corresponding base flows are numerical solutions of the axisymmetric boundary-layer equations in cylindrical coordinates. A high-order numerical discretization scheme based on Chebyshev collocation and a global eigenvalue search are employed to solve the corresponding stability equations. The two disturbance modes that are observed are of centrifugal (or Rayleigh) type and of shear-instability (or Kelvin–Helmholtz) type. The most amplified shear instabilities with higher azimuthal wavenumber possess a long-axial-wavelength character and are fed by the axial vorticity arising from the swirl component. Moreover, secondary and higher unstable modes corresponding to the centrifugal instability are observed. Viscosity has a slightly stabilizing effect on the shear-instability disturbances. Centrifugal-instability disturbances with short-azimuthal and short axial wavelengths are stabilized by viscous effects.