The interplay between turbulence structures and forces on bed spheres in open-channel flow through boulder arrays at various Froude numbers*

The Froude number (Fr) is a key parameter affecting turbulence structures, bedload transport, and bedforms in mountainous rivers. In this paper, the interplay between turbulence structures and forces on bed spheres in open-channel flow through boulder arrays at a Froude number range from 0.15 to 0.89 are reported. At low and intermediate Fr, the boulder top is above the water surface and time-averaged streamwise flow velocity, Reynolds shear stresses, and the turbulent kinetic energy (TKE) are relatively low in the wake of boulders. Conversely, at high Fr values, the boulders are submerged, hence the flow separates at the boulder crest, creates vertical recirculation and reattaches on the bed downstream, resulting in an area of elevated Reynolds shear stresses and TKE downstream of the boulders. Two dominant turbulence structures are observed: (i) flapping of boulder wakes with a characteristic length of 2.1 times the boulder diameter (D) at low and intermediate Fr and (ii) an upstream oriented hairpin vortex with a length scale of 1.0D at high Fr. These turbulence structures influence hyporheic exchange downstream of boulders within a limited region of x/D < 2.0. In other locations, hyporheic flow is driven by downwelling flow immediately upstream of boulders with a wavelength larger than 2.9D. Finally, the normalised time-averaged hyporheic flux increases with increasing Fr, but decreases at higher Fr values once overtopping flow disrupts the formation of the boulder wake.

The lift (F_x) and drag forces (F_z) on the top layer of bed spheres and their connection to nearby turbulence are further investigated. The time- and space- averaged F_x and F_z account for approximately 50% and 20% of the unit shear force, respectively, within a 10% variation at different Fr. The double-averaged drag and lift force fluctuations reach up to 130% and 90% of the unit shear force, respectively. The pre-multiplied spectra of force fluctuations reveal three wavelengths: (i) short (1.6D) , (ii) intermediate (4.0D) , and (iii) large wavelengths (4.5D). These correspond to hairpin vortices, flapping of boulder wakes, and hyporheic flow, respectively, evidenced by the pre-multipled spectra of the streamwise and vertical velocity fluctuations. Cross-correlations between force and velocity fluctuations indicate that forces on spheres in the boulder wakes are controlled by hyporheic flow at high Fr, and by boulder flapping at intermediate Fr. Finally, sediment deposition regions are predicted based on three types of criterions: the near-wall shear stress, the time-averaged forces, and the instantanedous forces, among which regions based on the instantaneous forces align inspiringly well with the deposition patterns observed by Papanicolaou et al. (2018) at different Fr.