The largest-scale vortices in turbulent boundary layers are hairpin vortices

Abstract

We examine two datasets of high-Reynolds-number turbulent boundary layers. One is a new dataset obtained by direct numerical simulations on the K computer, and the other is a dataset examined in our previous studies. By using these two datasets, we investigate the shape and sustaining mechanism of the largest-scale vortices in turbulent boundary layers. For this purpose, we identify the largest-scale structures by a coarse-graining method. First, visualizations in physical space show that vortices as large as the boundary layer thickness are hairpin-like. This explains the disappearance of smaller-scale hairpin vortices as the Reynolds number increases. Second, to quantitatively show the dominance of hairpin vortices at the largest scale, we take an average, conditioned by the existence of the low-speed structures at the height of the boundary layer thickness, of the second invariant of the coarse-grained velocity gradient tensor. This simple procedure, indeed, reveals a (largest-scale) hairpin vortex. It is also verified that a low-speed structure is located between the legs of the hairpin vortex.