Sensitivity analysis of the periodic orbits of plane Couette flow

In the last decade, concepts from dynamical systems have been applied to gain insight onto transition to turbulence in shear flows, such as pipe and plane Couette flow. For the latter, several nontrivial equilibrium solutions, travelling waves and periodic orbits were found, enabling the analysis of transition from a new perspective. In this contribution, we study the sensitivity of unstable periodic orbits in Couette flow. These limit cycles are dominated by the self-sustained interaction between vortices and streaks. By applying the Floquet analysis, we calculate the flow Lyapunov exponent; investigating the most unstable Floquet modes and the related adjoint modes, we analyze the eigenvalue sensitivity to localized structural perturbations over the orbit period. Preliminary results confirm that the core of the instability coincides with the region where the streaks are bent, in agreement with previous numerical results. In the final contribution the analysis will be completed by considering the sensitivity of the limit-cycle frequency and amplitude to feedback forcing.