Nonlinear global modes in miscible coreannular flows

We perform linear stability analyses and nonlinear simulations of variable viscosity, miscible coreannular flows in cylindrical tubes. For high viscosity ratios, these flows are found to be absolutely unstable, and they exhibit intrinsic oscillations different from the forcing frequency. These self-sustained oscillations give rise to nonlinear global modes. In the supercritical regime, with the core radius being the critical parameter, the nonlinear global mode frequencies match the linear absolute frequencies. This is in accordance with theory when the absolute frequencies are evaluated for the parameters at the inlet. We compare our simulations with recent experiments and observe excellent agreements.