On the ejection-induced instability in Navier-Stokes solutions of unsteady separation

Numerical solutions of the flow induced by a thick-core vortex have been obtained using the unsteady, two-dimensional Navier-Stokes equations. The presence of the vortex causes an adverse pressure gradient along the surface, which leads to unsteady separation. The calculations by Brinckman and Walker for a similar flow identify a possible instability, purported to be an inviscid Rayleigh instability, in the region where ejection of near-wall vorticity occurs during the unsteady separation process. In results for a range of Reynolds numbers in the present investigation, the oscillations are also found to occur. However, they can be eliminated with increased grid resolution. Despite this behaviour, the instability may be physical but requires a sufficient amplitude of disturbances to be realized.