Competing instabilities of rotating boundary-layer flows in an axial free-stream

In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone, defined by half-angle ψ<40°, is used for the first time to model the problem when an enforced oncoming axial flow is introduced. The resulting similarity solution represents the basic flow more accurately than previous studies in the literature. This mean flow field is subsequently perturbed leading to disturbance equations that are solved via numerical and analytical approaches, importantly yielding favourable comparison with existing experiments. Meanwhile, a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics of broad rotating cones, defined by half-angle ψ>40°, in axial flow.