BOUNDARY-LAYER TRANSITION ON ROTATING CONES

Dr. Stephen Garrett (Maths Dept., University of Leicester)

I will describe progress in identifying a new mode of instability within the boundary-flow over 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 Gortler-type spiral vortices. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics of broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is presented and a preliminary asymptotic analysis summarised which identifies a centrifugal mode within the boundary-layer flow over slender cones.