Computation of Bed Shear stress from Velocity Measurements in Gradually Varying Bed Roughness

Rivers originate from highlands or mountains and flow towards the sea or ocean. Along the course of a river, the streambed consisting of local geologic materials changes from place to place; for instance, large boulders in mountains, cobbles to very coarse gravels in foothills, coarse sand to fine sand in flood plains and coarse silt to very fine clay near to estuary are evident. Hence, the gradual change in bed roughness is a natural phenomenon. Understanding of this phenomenon in open-channel flows is an important aspect in hydraulic engineering. Several studies were performed in closed conduits when the change in bed roughness takes place abruptly. However, a few experimental studies were so far performed to investigate the gradual change in bed roughness in an open-channel flow. Therefore, the effects of alteration of bed roughness on the spatial distribution of local bed shear stress in an open-channel flow need further investigation.

This study is focused on the variation of bed shear stresses with downstream distance owing to a gradual change in bed roughness. An experimental study was conducted in a laboratory flume, where the bed roughness was gradually changed from smooth (d₅₀ = 1.53 mm) to rough (d₅₀ = 17.97 mm) over a stretch of 800 mm along the downstream length. Here, d₅₀ is the median sediment size. A linear variation of bed roughness from d₅₀ = 1.53 to 17.97 mm was considered, indicating that the intermediate bed roughness has four different sediment sizes (d₅₀ = 2.82, 6.2, 10.55 and 14.4 mm), each of which prevails over a length of 200 mm. Experiments were conducted for two different flow Froude numbers of 0.2 and 0.3. The velocity measurements were taken with a two-dimensional Particle Image Velocimetry (PIV) system. Several methods were proposed to accurately predict the bed shear stress, since its determination in a topographical change in bed roughness remains a challenging task (Clauser, 1954; Dyer, 1986; Kim et al., 2000). In this study, the local bed shear stress was evaluated from four distinct methods; for instance, the log-law, the Reynolds shear stress, the vertical turbulence intensity and the turbulent kinetic energy methods. These methods provided different results owing to certain discrepancies that are attributed to the boundary conditions and the local flow structures resulting from the bed roughness.

Key Words: Fluvial Hydraulics, Turbulent Flow, Open-Channel Flow, Bed Shear Stress