Turbulence Anisotropy in The Flow Layers of an Open-Channel Flow over a Rough Bed

The flow field in open channels can be classified into different layers according to specific characteristics, such as the velocity distribution and the balance between production and dissipation of turbulent kinetic energy. Considering the velocity distribution and starting from the bed up to the water surface, it is possible to define the following zones: roughness layer, intermediate layer and free surface layer.

The aim of this study is to verify the existence of turbulence anisotropy in the different flow layers on the basis of the two-dimensional (2D) second-order structure function.

An experimental study was conducted in a recirculating rectangular 9.66 m-long, 48.5 cm-wide tilting flume at the Laboratorio “Grandi Modelli Idraulici”, Università della Calabria, using 2D non-intrusive Particle Image Velocimetry (PIV) measurements. A 7 m-long, 12 cm-deep recess box, located at about 1 m from the flume inlet, was filled in with coarse gravel having a unimodal distribution, with median diameter d₅₀ = 17.98 mm and geometric standard deviation σ_g = 1.4. The bed was screeded to guarantee the same slope as the flume bottom equal to 1.5 ‰. In order to reconstruct the topography in detail, the bed surface was acquired with the photogrammetry technique and a 3D Terrestrial Laser Scanner. The velocity measurements were taken in a vertical plane along the flume centerline at the abscissa x = 6.50 m in the streamwise direction, where the flow was uniform. During the experiments the flow depth (h ≈ 12 cm) was controlled by an adjustable tailgate, with a constant flow discharge of about 0.020 m³·s^-1. The PIV system consisted of a 12 bit CCD camera, with 2048 x 2048 square pixels, and a frame rate of 15 Hz, as well as a double-pulse Nd:YAG laser (pulse energy of 200 mJ at a wavelength of 532 nm); 3000 image couples were acquired, with a measurement area of 174 x 174 mm² and a spatial resolution of 1.36 mm in both the vertical and streamwise directions.

Initially, the resulting instantaneous velocities were used to determine vertical profiles of the double-averaged (DA) streamwise velocity and the turbulence parameters, specifically the spatially averaged (SA) viscous shear stress and Reynolds shear stress. Thus, 2D second-order structure functions were calculated for each layer, revealing that they can be used as a tool to investigate the development of the turbulent anisotropy from the water surface to the rough bed.