Transition mechanisms within the boundary-layer flow over slender vs. broad rotating cones

We describe progress in classifying the convective instability characteristics of the boundarylayer flow over the family of rotating cones. Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a centrifugal instability mode that dominates over slender cones and manifests as Görtler-type spiral vortices. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is introduced and an asymptotic analysis summarized which identifies such a centrifugal mode.