Optimisation and control of boundary layer flows

Abstract: Both optimal disturbances and optimal control are studied by means of numerical simulations for the case of the flat-plate boundary-layer flow. The optimisation method is the Lagrange multiplier technique where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier–Stokes equations. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. The optimal disturbances for spanwise wavelengths of the order of the boundary layer thickness are streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. Control is applied to the bypass-transition scenario with high levels of free-stream turbulence. In this scenario low frequency perturbations enter the boundary layer and streamwise elongated disturbances emerge due to the non-modal growth. These so-called streaks are growing in amplitude until they reach high enough energy levels and breakdown into turbulent spots via their secondary instability. When control is applied in the form of wall blowing and suction, within the region that it is active, the growth of the streaks is delayed, which implies a delay of the whole transition process. Additionally, a comparison with experimental work is performed demonstrating a remarkable agreement in the disturbance attenuation once the differences between the numerical and experimental setup are reduced.