Very large-scale motions in a turbulent boundary layer

Direct numerical simulation of a turbulent boundary layer with \textit{Re}$_{\theta}$=2560 was performed to investigate the spatially coherent structures associated with very large-scale motions (VLSMs). Inspection of the three-dimensional instantaneous fields showed that groups of hairpin vortices are coherently arranged in the streamwise direction and that these groups create significantly elongated low- and high-momentum regions with large amounts of Reynolds shear stress. Adjacent packet-type structures combine to form the VLSMs; this formation process is attributed to continuous stretching of the hairpins, coupled with lifting-up and backward curling of the vortices. We employed the modified feature extraction algorithm to identify the properties of the VLSMs of hairpin vortices. Patches with lengths greater than 3$\sim $4\textit{$\delta $} account for more than 40{\%} of all the patches and these VLSMs contribute approximately 45{\%} of the total Reynolds shear stress. Finally, the application of linear stochastic estimation to the conditionally averaged flow field demonstrated the presence of packet organization in the form of a train of packets in the logarithmic layer.