Very-large-scale motions in a turbulent boundary layer

Abstract

Direct numerical simulation of a turbulent boundary layer 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. The main simulation was conducted by using a computational box greater than 50δo in the streamwise domain, where δo is the boundary layer thickness at the inlet, and inflow data was obtained from a separate inflow simulation based on Lund's method. 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. 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. We employed the modified feature extraction algorithm developed by Ganapathisubramani, Longmire & Marusic (J. Fluid Mech., vol. 478, 2003, p. 35) to identify the properties of the VLSMs of hairpin vortices. In the log layer, patches with the length greater than 3δ–4δ account for more than 40% of all the patches and these VLSMs contribute approximately 45% of the total Reynolds shear stress included in all the patches. The VLSMs have a statistical streamwise coherence of 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 demonstrated the presence of packet organization in the form of a train of packets in the log layer.

Transitional–turbulent spots and turbulent–turbulent spots in boundary layers

“…Other higher-level and larger-scale structures in the hierarchy (57)(58)(59) are not the focus of this paper. However, we note that the wake region ð0.5 < y=δ < 1Þ and the BTFTI region are densely populated by groves of concentrated large-scale hairpin vortices (Movie S7).…”

Scale growth of structures in the turbulent boundary layer with a rod-roughened wall

“…They interpreted that the apparent wavering of the VLSM on a scale of O(6δ) in the turbulent boundary layer (TBL) is induced as a consequence of spanwise offset LSMs rather than through sinusoidal perturbation of an otherwise straight, streamwise-aligned sequence of LSMs. Through time-evolving instantaneous fields, Lee and Sung 6 and Lee et al 9 provided clear evidence of the formation of VLSM in which adjacent packet-type structures combine to form VLSM on the order of O(18δ), as conjectured by Kim and Adrian. 10 Due to the significant importance of LSMs in wall-bounded turbulent flows, extensive studies of structures over rough-wall TBLs have been performed.…”

“…[1][2][3] These structures correspond to bulges or hairpin packets of large-scale motions (LSMs) with streamwise extents on the order of 1-3δ and very-largescale motions (VLSMs) with sizes in the range of 10-30δ, where δ is the boundary layer thickness. [1][2][3][4][5][6] Hairpin packets consist of a coherent group of hairpin vortices aligned along the streamwise direction. 5 These structures create elongated low-momentum regions beneath them which are bounded in the spanwise direction by high-momentum regions.…”

Coherent structures in statistically-stationary homogeneous shear turbulence

“…Similarly, Sillero et al (2014b) found that the self correlation of u in the wall parallel plane conditioned to u < 0 is longer than that conditioned to u > 0, independent of the wall distance. But results in Lee & Sung (2011) It is well accepted that closer to the wall structures are smaller while the opposite when farther away from the wall (Jiménez, 2012). So the downward moving v is supposed to bring large scales to the near wall region while the opposite for the upward v, i.e.…”