Transition to turbulence over oriented superhydrophobic riblets.

Superhydrophobic surfaces exhibit numerous interesting properties such as reduced friction or a delay in the transition to turbulence. This work aims to investigate the underlying mechanisms leading to these properties for 45°-oriented super-hydrophobic riblet roughnesses coated on the walls of a channel flow. The surface is modelled with a homogenization technique yielding a set of effective boundary conditions. Modal and non-modal stability analysis is obtained. A strong asymmetry of the neutral curve can be observed with the presence of two unstable branches in the β<0 region. Transient growth is also affected: maximum gain is obtained for a small but non-zero α and for β<0, thus inducing oblique optimal initial perturbations. Transition to turbulence is studied through direct numerical simulation (DNS) for both unstable branches. Two different transition scenarii are identified: the upper branch is governed by modal primary and secondary instability while the lower branch relies on non-modal mechanisms such as transient growth.