Very-large-scale motions in turbulent flows

Abstract

Direct numerical simulation (DNS) of a turbulent boundary layer (TBL) was performed to investigate the spatially coherent structures associated with very large-scale motions (VLSMs). The Reynolds number was varied in the range Reθ=570~2560. 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. Adja-cent 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. The growth of the spanwise scale of the hairpin packets occurs continuously, so it increases rapidly to double that of the original width of the packets. The VLSMs have a statistical streamwise coherence on the order of ~6δ; the spatial organization and coherence decrease away from the wall, but the spanwise width increases monotonically with the wall-normal distance. Finally, the application of linear stochastic estimation (LSE) demonstrated the presence of packet organization in the form of a train of packets in the log layer. DNS of a fully developed turbulent pipe flow was performed to investigate the similarities and differ-ences of VLSMs to those of TBL flows. The Reynolds number was set to ReD=35000, and the computational domain was 30R in length. The most obvious differences that arose in this comparison were that the stream-wise length of the structures in the pipe flow grew continuously beyond the log layer. In addition, the maxi-mum length of the VLSMs increased up to ~30δ with a much larger population of long structures (>3δ) than was present in the TBL flows, thereby increasing the length scale. Because an irrotational flow with a high momentum in the outer region of the TBL extended to the logarithmic layer, break-down of the streamwise co...