Abstract
Numerical solutions of the unsteady, two-dimensional Navier-Stokes equations are considered for the flow induced by a thick-core vortex. The adverse pressure gradient imposed on the surface by the vortex leads to unsteady separation. The presence and nature of an instability that may arise during the unsteady separation process is considered. The instability arises in the form of small-scale oscillations in vorticity and streamwise pressure gradient along the wall, and the dominant wavenumber of the instability is O(Re), consistent with a Rayleigh-type instability. The existence of a Rayleigh instability is confirmed through evaluation of the Rayleigh equation for velocity profiles obtained from a boundary-layer calculation, and the dominant wavenumber of the instability agrees very closely with that predicted by the Rayleigh solutions.
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