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Global instabilities computations of flow past a row of cylinders

In this talk we consider the onset of global instability in the flow past a row of circular cylinders placed in an oncoming uniform stream. A hybrid spectral method is used to first compute the steady flow and then investigate its linear stability by solving a generalised eigenvalue problem. Results have been obtained for the various mode classes, and our results show that for the odd-even modes which correspond to anti-phase oscillatory motion about the mid-plane between the cylinders, and are the ones most extensively studied in the literature, the effect of blockage has a marginal inuence on the critical Reynolds numbers for instability. This is in sharp contrast to results cited in many studies with a fully developed inlet flow past a cylinder placed between confining walls. We are also able to nd other unstable modes and in particular for low blockage ratios, the odd-odd modes which correspond to in-phase oscillatory motion about the mid-plane between the cylinders, are the first to become unstable as compared to the odd-even modes, and with much lower frequencies.
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