Turbulent junction flow characteristics upstream of boulders mounted atop a rough, permeable bed and the effects of submergence

Abstract

While turbulent flow characteristics in the region upstream of wall-mounted obstacles (often called the junction region) are well described for many engineering systems, uncertainty remains about flow characteristics upstream of the large, immobile boulders that are commonly found in steep gravel-bed streams. This uncertainty is largely due to the unique bed features (e.g., relatively large bed roughness, a permeable bed) and hydraulic characteristics (e.g., variable submergence) present at boulders, which may affect flow characteristics. This study reports results of laboratory volumetric particle image velocimetry (PIV) experiments performed upstream of model boulders for fully submerged (FS) and partially submerged (PS) conditions. Several atypical junction flow characteristics were documented. Mean-flow reversal and spiraling streamlines (commonly associated with horseshoe vortices) were not documented, though limitations in near-bed measurement extents contributed to this result in several cases. Nevertheless, modest increases in local rotation rate (assessed via vorticity magnitude and swirling strength) were observed near where the horseshoe vortex is typically expected. Mean-flow data also suggest that notable mass flux into the permeable bed occurred upstream of boulders. Several effects of submergence on junction flow characteristics were also identified. Compared with the FS condition, the PS condition exhibited more rapid deceleration of the mean streamwise velocity, stronger downward velocities near the bed that extended over a wider transverse area, stronger increases of the near-bed turbulent kinetic energy, and oppositely signed streamwise-vertical Reynolds stresses near the water surface. The improved understanding of flow upstream of boulders provided here will aid future river engineering and restoration efforts.

Graphical abstract

Appendix: Measurement uncertainty quantification

Uncertainty in instantaneous velocity measurements, ${\epsilon }_{u}$, was estimated using the fluctuating velocity divergence according to ${\langle {\left(\partial {u}_{i}^{\prime}/\partial {x}_{i}\right)}^{2}\rangle }^{1/2}=\sqrt{3/2}{\epsilon }_{u}/{\Delta }_{PIV}$, where $\langle \rangle$ denotes the ensemble average (Zhang et al. 2017). For each of the no boulder datasets, ${\langle {\left(\partial {u}_{i}^{\prime}/\partial {x}_{i}\right)}^{2}\rangle }^{1/2}$ was estimated for 100 random instantaneous measurement fields. The corresponding estimates of ${\epsilon }_{u}$ were 25.9 mm/s, 10.8 mm/s, and 11.5 mm/s (or ${\epsilon }_{u}/U$ equal to 3.1%, 1.3%, and 2.6%) for the CV1, CV2, and CV3 experiments, respectively. These ${\epsilon }_{u}$ values corresponded to 0.68 voxel, 0.26 voxel, and 0.40 voxel displacement uncertainties, respectively, which are comparable to values reported in the literature for volumetric PTV and tomographic PIV measurements (Zhang et al. 2017; Bhattacharya and Vlachos 2020). It should be noted that this ${\epsilon }_{u}$ estimation method returns one uncertainty value, whereas uncertainty is expected to be highest in the direction of camera viewing and lower in the other two directions (Bhattacharya and Vlachos 2020). Uncertainties in instantaneous vorticity components (obtained with central differences) were estimated as ${\epsilon }_{\omega }=\frac{{\epsilon }_{u}}{{\Delta }_{PIV}}\sqrt{1-\rho (2{\Delta }_{PIV})}$, where $\rho \left(2{\Delta }_{{\text{PIV}}}\right)$ is the normalized cross-correlation of the measurement error at two grid points with a spatial separation of $2{\Delta }_{{\text{PIV}}}$ (Sciacchitano and Wieneke 2016). Since appropriate values of $\rho \left(2{\Delta }_{{\text{PIV}}}\right)$ should be determined based on synthetic data for a given processing algorithm (Sciacchitano 2019) and no known results are available for the methods used herein, the value 0.45 determined for 2D PIV by Sciacchitano and Wieneke (2016) was used. The corresponding estimates of ${\epsilon }_{\omega }$ are 11.3 s⁻¹, 7.3 s⁻¹, and 3.1 s⁻¹ (or ${\epsilon }_{\omega }{W}_{b}/U$ equal to 0.7, 0.5, and 0.4) for the CV1, CV2, and CV3 experiments, respectively.

Uncertainties in mean quantities were evaluated using uncertainty propagation (Sciacchitano and Wieneke 2016). Since the sampling frequency (89 Hz) is expected to yield correlated velocity fields, the effective number of independent samples, ${N}_{{\text{eff}}}$, for calculating uncertainty in statistics was estimated as ${N}_{{\text{eff}}}={T}_{{\text{dur}}}/2{T}_{{\text{int}}}$, where ${T}_{{\text{dur}}}$ is the sampling duration and ${T}_{{\text{int}}}$ is the integral time scale (Sciacchitano and Wieneke 2016). Values for ${T}_{{\text{int}}}$ in the approach flow were estimated according to $0.25{H}_{{\text{w}}}/U$, where the 0.25 factor accounts for the integral length scale near mid-depth (e.g., Nezu and Nakagawa 1993). Corresponding estimates of ${N}_{{\text{eff}}}$ are 1130 and 2080 for the FS and PS conditions, respectively. Employing the stated values of ${\epsilon }_{u}$, ${\epsilon }_{\omega }$, and ${N}_{{\text{eff}}}$, it was estimated that uncertainties in mean velocities were all less than 0.1% of $U$ and uncertainties in mean normalized vorticity, ${\epsilon }_{\overline{\omega }}{W}_{b}/U$, were all less than 0.02.