Direct numerical simulation of transition under free-stream turbulence and the influence of large integral length scales

Abstract

Under the action of free-stream turbulence (FST), elongated streamwise streaky structures are generated inside the boundary layer, and their amplitude and wavelength are crucial for the transition onset. While turbulence intensity is strongly correlated with the transitional Reynolds number, characteristic length scales of the FST are often considered to have a slight impact on the transition location. However, a recent experiment by Fransson and Shahinfar [J. Fluid Mech. 899, A23 (2020)] shows significant effects of FST scales. They found that, for higher free-stream turbulence levels and larger integral length scales, an increase in the length scale postpones transition, contrary to established literature. Here, by performing well-resolved numerical simulations, we aim at understanding why the FST integral length scale affects the transition location differently at low- and high turbulence levels. We found that the integral length scales in Fransson and Shahinfar's experiment are so large that the introduced wide streaks have substantially lower growth in the laminar region, upstream of the transition to turbulence, than the streaks induced by smaller integral length scales. The energy in the boundary layer subsequently propagate to smaller spanwise scales as a result of the nonlinear interaction. When the energy has reached smaller spanwise scales, larger amplitude streaks results in regions where the streak growth are larger. It takes longer for the energy from wider streaks to propagate to the spanwise scales associated with the breakdown to turbulence, than for those with smaller spanwise scales. Thus, there is a faster transition for FST with lower integral length scales in this case.