Depth-Averaged von Kármán Coefficient in Sediment-Laden Flows Using a Turbulent Kinetic Energy Balance

Abstract

Precise prediction of bed shear stress (τ0) and velocity profile in open channels is critical in various applications. This paper deliberates on the depth-averaged von Kármán coefficient in sediment-laden flows based on the turbulent kinetic energy balance. Based on the conservation equation for turbulence energy derived in the literature, a densimetric von Kármán coefficient in sediment-laden flows is proposed by modifying the von Kármán coefficient of clear-water flow and incorporating a densimetric Kolmogorov number. Sensitivity analysis of the theoretical bed surface datum to the estimated von Kármán coefficient is also performed. Eighty-two sets of laboratory experiments were conducted to investigate the near-bed velocity distribution for sediment-laden flow using ultrasonic Doppler velocity (UDV). Based on the findings of the study and published data by others, a formula that could be used to calculate the depth-averaged von Kármán coefficient for sediment-laden flow is proposed. Leveraging on this formula, a new velocity distribution relationship for two-dimensional (2D) turbulent sediment-laden flow is also developed. The formula for the depth-averaged densimetric von Kármán coefficient can be obtained when the depth-averaged sediment concentration and sediment density are known. The quality of the predicted velocity distribution had been tested with others and found to produce a good estimate of turbulent velocity profiles with suspended sediments.