The sharp but irregular interface that separates the instantaneous turbulent and irrotational flows is termed as the turbulent/non-turbulent interface (TNTI). TNTI can be widely observed in various types of flow, such as turbulent boundary layers, jets and combustion flame fronts. Due to its importance on the intermittency and entrainment process, TNTI has been widely explored in its geometry and dynamic properties (da Silva et al., 2014). Most of the studies focus on the TNTIs in smooth plane boundary layer, while few investigate the effects of wall shapes. However, the wall conditions in many engineering applications are complex and heterogeneous, which will induce large-scale heterogeneity (Barros and Christensen, 2014) and require further investigations. To shed new light on the intermittency and entrainment above complex surfaces, the TNTI over spanwise heterogeneity are investigated here with time-resolved stereoscopic PIV (TR-SPIV).
The model and TR-SPIV experimental set-up are shown in Fig. 1. The experiments are conducted in the low-speed water channel at Beijing University of Aeronautics and Astronautics. The spanwise distance S between two adjacent ridges is S/(δ) = 1.35, where (δ) is the spanwise-averaged boundary layer thickness. This spanwise distance is selected to induced strong secondary vortices (Vanderwel and Ganapathisubramani, 2015; Wangsawijaya et al., 2020). The Reynolds number based on the streamwise location x is Rex = 7.2×105. The field of view is around 2S×1.8S, and is captured by two CMOS cameras (2048×2048 pixel) with sampling rate as 500Hz. The averaged resolution is about 8 pixels per Kolmogorov scale (calculated at y/(δ) = 0.6), which is high enough for TNTI-related research (Borrell and Jimenez, 2016). The ´TNTI is detected by the magnitude of local enstrophy ω2/2, and the threshold is selected to be the value where changing the threshold has the smallest influence on the TNTI-mean-height (Watanabe et al., 2018).
The time-mean velocity and TNTI location are present in Fig.2(a). A pair of counter-rotating largescale secondary vortices (SVs) are induced over the ridge-type roughness. At the position where SVs induce upwash flow, a low-momentum pathway (LMP) can be observed, while the time-mean height of TNTI (yI) is brought higher. As a contrast, where downwash flow induces high-momentum pathway (HMP), (yI) is lower.
TNTI properties are further discussed from two aspect. The geometry properties are firstly investigated. The fractal dimension of the TNTI keeps as 2.3 along the spanwise direction. This value is consistent with the result over smooth plate (Borrell and Jimenez, 2016; Wu et al., 2020) and riblets plates(Cui et al., 2019),´ which indicates that the wall shapes do not influence the multiscale properties of the TNTI. The streamwise wavelength of the TNTI (λI) is further obtained by calculating the streamwise pre-multiplied spectrum of the TNTI. It is found that at each spanwise location, λI is identical to the wavelength of streamwise velocity fluctuation at the TNTI mean height. This shows that the large-scale fluctuation of TNTI is controlled by the large-scale streamwise velocity fluctuation structures. Secondly, the p.d.f. of TNTI instantaneous height is investigated, as shown in Fig. 2(b). It can be observed that the p.d.f. of TNTI height above LMP shows a negative skewness, while the p.d.f. above HMP skews positively. A closer look at instantaneous structures shows that the skewness is attributed to the different probability of Q2/Q4 events in LMP and HMP.
Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities
