The Stability and Transition of the Compressible Boundary-Layer Flow over Broad Rotating Cones

The subject of fluid flows over axisymmetric bodies has increased in recent times, as they can be used to model flows over a swept wing, spinning projectiles and aeroengines amongst other things. A better mathematical understanding of the transition from laminar to turbulent flow within the boundary layer could lead to an improvement in the design of such applications. We consider a compressible fluid flow over a rotating cone, defined by half-angle ψ. The mean flow boundary-layer equations are derived and we conduct a high Reynolds number asymptotic linear stability analysis. The flow is susceptible to instabilities caused by inviscid crossflow modes (type I ) and modes caused by a viscous-Coriolis balance force (type II ). Both are considered, along with the effects of changes in the cone half-angle, the magnitude of the local Mach number and the temperature at the cone wall. A surface suction along the cone wall is also analysed.