Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers

Abstract

Direct numerical simulations (DNS) of temporally developing turbulent boundary layers are performed with a wide range of Reynolds numbers based on the momentum thickness $Re_{\theta } = 2000$ – $13\,000$ for investigating the Reynolds number dependence of the turbulent/non-turbulent interface (TNTI) layer. The grid spacing in the DNS is determined carefully such that small-scale turbulent motions near the TNTI are well resolved. The outer edge of the TNTI layer, called the irrotational boundary, is detected with vorticity magnitude. The mean thicknesses of the TNTI layer, $\delta _{TNTI}$ , turbulent sublayer, $\delta _{TSL}$ , and viscous superlayer, $\delta _{VSL}$ , are found to be approximately $15\eta _{TI}$ , $10\eta _{TI}$ and $5\eta _{TI}$ , respectively, where $\eta _{TI}$ is the Kolmogorov scale taken in the turbulent region near the TNTI layer. The mean curvature of the irrotational boundary is also characterized by $\eta _{TI}$ . The shear parameter and the shear-to-vorticity ratio show that the mean shear effects near the TNTI layer are not significant for both large and small scales. The anisotropy tensors of Reynolds stress and vorticity suggest that the turbulence under the TNTI layer tends to be isotropic at high $Re_{\theta }$ , for which $\eta _{TI}/\delta \sim Re_{\theta }^{-3/4}$ is valid with the boundary layer thickness $\delta$ . The surface area of the irrotational boundary is consistent with the fractal analysis of the interface, where the fractal dimension $D_f$ is found to be $2.14$ – $2.20$ . The present results suggest that the mean entrainment rate per unit horizontal area normalized by the friction velocity varies slowly as $Re_{\theta }^{(3/4)(D_f-2)}$ for $Re_{\theta } \geq 4000$ .

Investigations on the turbulentnon-turbulent interface in supersonic compressible plate turbulent boundary layer

“…The comparison of interface thickness with previous results by Zhang et al. (2018 b , 2023) is shown in figure 15. It has been found that as the increases, the mean thickness of the TNTI remains almost unchanged within approximately (Zhang et al.…”

“…2022; Xu, Wang & Chen 2023; Zhang et al. 2023). It can be seen that in figure 6( a ) the present work is fitted well with previous results, while in figure 6( b ) there are some differences above .…”

“…Further, 15 % of the peak value of the derivative was chosen as the boundary to define the mean thickness of the TNTI, and the thickness of the viscous superlayer (VSL) and the turbulent sublayer (TSL) inside the interface was further divided through the relationship between the production term and the viscous diffusion term in the enstrophy transport equation. It was found that as the Reynolds number increases, the thickness of the interface and the VSL remain almost unchanged, approximately and 4–, respectively, where is defined as the Kolmogorov scale in the turbulence (Zhang, Watanabe & Nagata 2023).…”

Turbulent structures beneath semi-submerged simulated ice cover over smooth and rough bed in a shallow channel

“…This interface is dominated by small-scale-like instabilities, as observed from Figs. 3a-d, and can result in an intermittent flow behavior (Zhang et al, 2023). Due to the distinct separated shear layer observed for the smooth bed flow, this thin region persists until x/t = 1.5, but not visible for the rough bed case.…”

“…The shear layer interface at the leading-edge is dominated by small rollups akin to KH-type instabilities that enhance small-scale entrainment into the separated shear layer (Fang et al, 2022;Stella et al, 2017;Vadlamani et al, 2018). The small-scale instabilities grow along the interface and are eventually absorbed into the separation bubble (Wei et al, 2024;Zhang et al, 2023). It is obvious that the bottom roughness heavily impacted the separated shear layer beneath the cover.…”