Towards converged statistics in three-dimensional canopy-dominated flows

Multi-plane telecentric 2D particle image velocimetry (PIV) measurements were performed over and within the interstices of rough beds in an open-channel flow with low relative submergence. Two rough beds constituted of cubes and elongated cuboid obstacles in a square array were investigated with the same modified relative submergence. The telecentric method allowed the complete fluid space within the interstices and above to be measured without disturbing the flow. Nine planes were measured yielding a total of 17 planes by symmetry consideration. This allowed double-average computations to be performed with a 17 \(\times\) 17 horizontal spatial resolution yielding allowing to resolve adequately the shear stress terms contributing to the total shear stress. It is shown that subsampling with a coarse grid of 1 \(\times\) 5 yields acceptable spatially converged results, but only for the double-averaged longitudinal velocities. Together, the spatially averaged turbulent shear stresses and the dispersive stresses require a sampling of at least \(9\times 9\) within the canopy and \(5\times 5\) above for the errors relative to the total shear stress to remain below 5%. Above the canopy, the dispersive shear stress depends largely on the aspect ratio of the roughness obstacles, being much higher for the cubes than for elongated cuboids. Finally, the converged total shear stress is shown to yield the vertical integrated drag stress as well as the repartition of the flat-bed shear stress to the total shear stress.