Drag and Lift Forces on Bed Sediments in Open-Channel Flow Through Boulders at Various Froude Numbers

Abstract

The Froude number (Fr) is an important parameter that affects turbulence structures, bedload transport, and bedforms in mountain rivers. In a prior study by Liu et al. (2024, https://doi.org/10.1063/5.0222673), turbulence structures in open channel flow through a boulder array placed on seven layers of spheres (comprising the channel bed), with Fr ranging from 0.15 to 0.89, have been quantified. This paper investigates the drag (F_x) and lift (F_z) forces on the spheres of the top layer of the bed surrounding the boulders and their response to the boulder-induced turbulence and hyporheic flow. The time-averaged drag and lift forces (F_x and F_z) in the vicinity of boulders reach up to 6 and 4 times the reach-averaged shear force (F_sph), respectively, and their standard deviations are even higher, being 2.9 or 4.4 times the time-averaged forces, respectively. Consequently, maximum instantaneous forces on the surrounding bed spheres can approach values of an order of magnitude greater than F_sph. The pre-multiplied spectra of force fluctuations, which decompose the total fluctuations into components of different length scales, reveal three predominant contributions: (a) a 1.6D length-scale contribution at high Fr, (b) a 2.1D length-scale contribution at low and intermediate Fr, and (c) a 4.5D length-sale contribution at low and high Fr, where D is the boulder diameter. These correspond to elongated rollers, oscillating boulder wakes, and hyporheic flow, respectively. Cross-correlations between force and velocity fluctuations indicate that forces on the bed spheres in boulder wakes are governed by hyporheic flow at low and high Fr, and by vortex shedding at intermediate Fr. The contributions from hyporheic flow to total drag and lift force fluctuations are highest at high Fr, reaching up to approximately 30% and 50% locally, respectively. Finally, regions of sediment deposition are predicted based on three types of criteria: near-wall shear stress, time-averaged forces, and instantaneous forces, among which regions based on the instantaneous forces align remarkably well with the deposition patterns observed by Papanicolaou et al. (2018, https://doi.org/10.1029/2018jf004753) for different Fr.