Transition to turbulence over convex surfaces

Abstract

Although boundary-layer flows over convex surfaces are exponentially stable, non-modal mechanisms may enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instabilities in flows over convex surfaces is performed. The optimal disturbance in the steady case corresponds to alternating streaks and streamwise vortices of opposite sign that reinforce one another due to lift-up and centrifugal forces, respectively. The process repeats with a constant (naturally appearing) streamwise wavelength which is proportional to the square root of the radius. Unsteady disturbances achieve a higher optimal gain, compared to the steady case, as a result of the opposing effects of the lift-up and centrifugal mechanisms. Linear analysis shows that the curvature has a negligible effect on secondary instabilities. Direct numerical simulations of transient growth with and without secondary instabilities confirm the predictions obtained by the local stability theory. It is found that the presence of a secondary instability is not sufficient, on its own, to ensure transition to turbulence. Only sufficiently long and energetic streaks trigger the breakdown to turbulence.