Abstract

The common feature of boundary-layer flows subjected to free-stream turbulence (FST) is dominance of streamwise elongated structures , often called streaks or Klebanoff modes, whose secondary instability is precursor of laminar-turbulent transition. These structures are observed both experimentally and in the numerical simulations. Theoretically, appearance of these structures are explained by non-normality of the operator describing evaluation of small disturbances. Here, the streaks are the optimal respond of the boundary layer to initial perturbations or forcing. However, the role of optimal perturbations in generation of streaks in experiments and numerical simulations has been questioned arguing such optimal initial perturbations have not been observed in the experiments. In the present study, by means of a series of numerical simulations of flow over an airfoil subjected to FST , we quantify the role of optimal disturbance in generation of streaks observed in the simulations. This is done through projection of the flow fields at the leading edge onto optimal disturbances. Our results demonstrate that optimal disturbance growth is the main cause of growth of disturbances on the wing boundary layer. We consider four different FST conditions which are characterised by their intensity and integral length scales. In all cases the perturbed flow develops into elongated disturbances of high and low streamwise velocity inside the boundary layer, where their spacing has been found to be strongly dependent on the scales of the incoming free-stream vorticity. The disturbance growth is found to depend not only on the turbulence level, but also on the FST length scale. Particularly, higher disturbance growth is observed for our cases with larger length scales. This behaviour is attributed to the preferred wavenumbers that can exhibit maximum transient growth.