The meandering behaviour of large-scale structures in turbulent boundary layers

Abstract

This paper quantifies the instantaneous form of large-scale turbulent structures in canonical smooth-wall boundary layers, demonstrating that they adhere to a form that is consistent with the self-sustaining streak instability model suggested by Flores & Jiménez (Phys. Fluids, vol. 22, 2010, 071704) and Hwang & Cossu (Phys. Fluids, vol. 23, 2011, 061702). Our motivation for this study stems from previous observations of large-scale streaks that have been spatially locked in position within spanwise-heterogeneous boundary layers. Here, using similar tools, we demonstrate that the randomly occurring large-scale structures in canonical layers show similar behaviour. Statistically, we show that the signature of large-scale coherent structures exhibits increasing meandering behaviour with distance from the wall. At the upper edge of the boundary layer, where these structures are severely misaligned from the main-flow direction, the induced velocities associated with the strongly yawed vortex packets/clusters yield a significant spanwise-velocity component leading to an apparent oblique coherence of spanwise-velocity fluctuations. This pronounced meandering behaviour also gives rise to a dominant streamwise periodicity at a wavelength of approximately $6\unicode[STIX]{x1D6FF}$. We further statistically show that the quasi-streamwise roll-modes formed adjacent to these very large wavy motions are often one-sided (spanwise asymmetric), in stark contrast to the counter-rotating form suggested by conventional conditionally averaged representations. To summarise, we sketch a representative picture of the typical large-scale structures based on the evidence gathered in this study.

Hairpin vortices in the largest scale of turbulent boundary layers

“…9(b) is shown. the result by Kevin et al (2019a) that the conditional averaged velocity elds are one-sided-rotating (quasistreamwise vortices) or counter-rotating ow (hairpin vortices). We also see that these vortices form packets along the LSM, which is also consistent with the observations of LSM by PIV (e.g.…”

Energy transfer structures associated with large-scale motions in a turbulent boundary layer

“…For an a priori test of energy transfer behaviour, the preliminary issue is to divide the scale space into 'resolved' and 'unresolved' parts. Due to the strong inhomogeneity and anisotropy of LSMs (Chandran et al 2017;Kevin, Monty & Hutchins 2019), 2-D or 3-D isotropic filters, which were commonly used to separate small scales from large ones (Xiao et al 2009;Wang et al 2018a;Motoori & Goto 2019;Dong et al 2020), cannot be applied here. In the present work, we will use an anisotropic 2-D filter for scale separation.…”

“…The key concept is to break the statistical symmetry along the spanwise direction, which has not been taken into account in previous studies (Piomelli et al 1996;Natrajan & Christensen 2006;Hong et al 2012;Dong et al 2020). Recently, Kevin et al (2019) have clarified the significance of the meandering motion of LSMs/VLSMs in the log layer and above. Our analysis will demonstrate that the wavy pattern of LSMs, other than streamwise aligned sweep and ejection motions (Natrajan & Christensen 2006), contribute a significant portion of the interscale energy transfer.…”

Large-scale coherent structures in compressible turbulent boundary layers

“…However, for the wall-normal locations 0.1 and 0.2 the meandering intensity variation is rather small (Kevin et al. 2019).…”