Modal and nonmodal stability of the laminar flow in a channel with longitudinal riblets

The influence of a surface covered with riblets on laminar-turbulent transition in channel flow is investigated through modal and non-modal stability analysis of n-periodic systems, allowing to take into account detuned long-wavelength instabilities. For large riblet spacing, a wavenumber lock-in regime is observed, in which the wavelength of the optimal streaks is controlled by the riblet spacing, and the streaks amplitude is modulated in the spanwise direction via a beating mechanism, as in geometric frustration. Moreover, in the presence of harmonic forcing, riblets lead to the development of oblique waves that may trigger an early transition.