Flows over convex surfaces undergoing transient growth

Curved surfaces are convex in most applications, such as airfoils, compressor and turbine vanes, while concave surfaces are less common. Nevertheless, boundary-layer flows over convex surfaces have received considerably less attention than flows over concave surfaces since they are exponentially stable. In these stable flows non-modal mechanisms may lead to significant transient growth, which can make the flow susceptible to secondary disturbances. The mechanism of transient growth over a convex surface is analyzed and a parametric investigation is performed. It is found that the optimal disturbance corresponds to alternating streaks and rolls of opposite sign which reinforce one another via the lift-up and centrifugal forces, respectively. For a given curvature the optimal disturbance is found to be unsteady as a result of the opposing effects of the lift-up and centrifugal mechanisms. The predictions obtained using local stability theory are verified by direct numerical simulations.