On the stability of boundary-layer flow over a rotating cone in an enforced axial free stream

Studies into the boundary-layer stability of rotating cones in an axial free stream have considered both cases of broad-angled cones and slender-angled ones. This distinction is made due to the findings that the dominant instability in the quiescent-fluid case results from different physical mechanisms for broad and slender cones. These investigations made use of an Orr-Sommerfeld-type analysis derived from the assumption of a small perturbation to a similarity-type solution for the mean fluid flow around the cone. In this work, we investigate the efficacy of a combination of sophisticated numerical techniques to find the basic flow, using ideas both from automatic differentiation and spectral collocation methods, to maximise the accuracy of the obtained solution. We inspect the solutions obtained for the Orr-Sommerfeld system in this setting and compare them to the results from previous studies.