Scalings for transition of the boundary layer on a rotating slender cone in axial flow

Abstract The boundary layer on rotating slender cones exhibits a centrifugal instability both in still fluid and at low axial velocity, in contrast to broad cones (and disks) that are mainly susceptible to a cross-flow instability. Here the influence of axial flow on the transition on a slender rotating cone with an apex angle of 15 degrees is studied in a towing tank using reflective flakes as tracers. A novel technique is used to evaluate the reflected light intensity from the flakes in terms of its probability density distribution (pdf) and root-mean-square (rms) to determine where transition occurs at different axial flow velocities. It is shown that axial flow stabilizes the boundary layer and our experiments together with others indicate that a Görtler number based on a length scale proportional to the boundary layer thickness is constant at transition for slender cones.