A data-driven optimal disturbance procedure for free-stream turbulence induced transition

The investigation of free-stream turbulence induced transition by means of simple and effective numerical methods traditionally represents a major challenge in the aerodynamic field. In this work, a data-driven algorithm aimed at obtaining optimal forcing and response concerning free-stream turbulence induced boundary layer transition is introduced. The method, referred to as Data-driven Optimal Disturbance (DOD) in the following, relies on dynamic mode decomposition to compute the linear matrix responsible for disturbance evolution in the streamwise direction and opens the possibility for optimal disturbance analysis in an equation-free manner. The procedure has been applied to high-fidelity large-eddy simulation (LES) results concerning zero pressure gradient flows. Four different combinations of turbulence intensity Tu and integral length scale Lg have been adopted as boundary conditions to investigate the sensitivity of the transition route to the free-stream turbulence properties. Overall, DOD applied within the transitional region identifies highly energetic turbulent scales embedded in the free-stream as the optimal forcing inducing the formation of streaky structures within the boundary layer. Furthermore, streaky structures characterized by the same spanwise wavelength observed in the LES results are identified by DOD as the boundary layer response to the optimal forcing. Finally, the amplification of disturbances provided by DOD along the streamwise direction clearly resembles the well-established transient growth. Thus, DOD appears a useful tool to analyze the free-stream turbulence induced transition of boundary layers by a simple equation-free algorithm merely based on data analytics.