A model for Reynolds stresses in boundary layer transition subjected to free-stream turbulence

We present a model for the Reynolds stresses in the transitional boundary layers subjected to high-level free-stream turbulence in this work. Our investigation reveals that to accurately quantify the profiles of all Reynolds stress components, it is imperative to model three key physical processes. The diffusion process of free-stream turbulence is crucial for quantifying the mean profiles of Reynolds stress components in the early stage of the laminar region. The coupling mechanism between the length function is used to model the growth of the streamwise Reynolds stresses at the beginning of the laminar region. The third model incorporates the well-known Klebanoff model, which is incorporated to facilitate the rapid growth of streamwise intensity. We derive and validate the coupling mechanism between length functions corresponding to Reynolds stress components by carefully considering the balance of the turbulent kinetic energy equation and utilizing the power laws of length functions. Our model demonstrates a satisfactory agreement with direct numerical simulation data and experimental data of transitional boundary layer flows subject to high-level free-stream turbulence, providing a novel approach to comprehending the generation and evolution of turbulent intensities induced by free-stream turbulence. This work may help develop a more accurate transition model for engineering applications.