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Stability analysis of vortex breakdown bubbles

Matthew Juniper (with Ubaid Qadri and Dhiren Mistry)

We analyse the local and global stability of a swirling vortex breakdown bubble and the wake behind it. The local analysis shows that the flow contains two absolutely unstable regions, each with a different wavemaker position and global frequency.

Through overlap of the direct and adjoint eigenfunctions, the global analysis reveals that the upstream region is the wavemaker of the linear global mode. Nonlinear results reveal, however, that the downstream region is the wavemaker of the nonlinear global mode. This discrepancy might be explained by condidering the two regions as coupled oscillators with different saturation amplitudes.

Figure caption: Base flow; absolute growth rate; direct global mode; adjoint global mode; structural sensitivity to forcing in the direction of the velocity; max structural sensitivity (wavemaker region)