A geometrical criterion for absolute instability in separated boundary layers

Laminar separation bubbles on airfoils and low-pressure turbines are generally expected to be dominated by convective inflectional instability. However, absolute instability is possible under certain circumstances, which may lead to important changes in the laminar-turbulent transition, reattachment processes, and their impact on the aerodynamics. This paper revisits the absolute/convective instability properties of different families of boundary-layer velocity profiles with a reversed flow region. A new methodology is employed in the analysis, which incorporates an additional equation to the classic Rayleigh's equation governing inviscid instability. This allows for the direct recovery of the zero-group-velocity disturbance waves that govern the absolute/convective behavior, at an unprecedented low computational cost that enabled the large parametric study performed here. Present results show that while the peak reversed flow or wall-normal extent of the reversed flow impact the instability character, criteria based on any of them are generally not valid. A new criterion is proposed, based on the relative position of the inflection point: inviscid inflectional instability becomes of an absolute kind when the inflection point is located inside of the recirculation region. Absolutely unstable velocity profiles are identified with peak reversed flow as low as 10% of the free-stream velocity, a value substantially smaller than thresholds previously proposed in the literature.