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

Abstract

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.