Global Low-Frequency Oscillations in a Separating Boundary-Layer Flow

A separated boundary layer flow at the rear of a bump is considered and two-dimensional flow states at increasing Reynolds numbers are computed using a nonlinear continuation procedure for the stationary Navier Stokes system. The global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The analysis reveals non-normal modes which are able to describe localized initial perturbations associated with large transient energy growth. At larger time a global low-frequency oscillation is found accompanied with periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier Stokes time integration and is shown to trigger nonlinear 'flapping' typical for separation bubbles.