The effect of rounding corners or cutting edges on the absolute/convective instability properties of mixing layers

We revisit the inviscid spatio-temporal stability properties of mixing layers. Earlier comparisons of the dispersion relations pertaining to the broken line model and the hyperbolic tangent profile have shown that the temporal stability properties are mainly governed by the velocity difference and the shear layer thickness, and that they are very robust to the details of the velocity profile. The situation however dramatically changes when one considers the spatio-temporal stability properties of these two limiting cases, which were shown to differ significantly. With the aim to better understand these strong differences, we introduce a family of velocity profiles that continuously spans from the broken line model to the tanh profile. We show that the momentum thickness appears as an important parameter that helps better predicting the absolute/convective properties of a given mixing layer.