Numerical Simulation of Tollmien–Schlichting Wave Generation by Flow Turbulence

The disturbances generated by external turbulence in the shear layer on a flat plate suddenly set in motion are found. As the initial conditions, turbulent flow found using direct numerical simulation of the development of isotropic homogeneous turbulence is used. The solution obtained models laminar-turbulent transition in the boundary layer on a flat plate under relatively low free-stream turbulence when the transition is caused by Tollmien–Schlichting waves. The solution makes it possible to describe the process of generating various disturbances, namely, low-frequency streaky structures and instability waves and also their development in the initial stage of laminar-turbulent transition. Based on the processing of the obtained results, a simple model is proposed that relates the spectra of instability waves in the boundary layer and turbulent pulsations in free-stream flow. The dependences of the initial amplitude of instability waves and their critical amplification factors (N-factors) on the degree of flow turbulence are also obtained.