For one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear equations by the discretization of the one-dimensional dynamic equation for open-channel networks. The results of the computations using the dynamic and energy equations were compared for an arbitrarily chosen problem. Also, the reasons for the differences between the solution of the dynamic and energy equation were investigated.
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We analyse experimental measurements of turbulent open-channel flow over hydraulically-smooth and transitionally-rough beds using the double-averaging methodology. Oil with a viscosity of 15×10-6 m2/s is used instead of water so that transitional-range roughness Reynolds numbers can be achieved with large (11.1 mm) roughness elements, allowing spatial variations in the mean velocity field to more easily be measured. Distributions of double-averaged velocities, turbulence intensities, form-induced intensities, and viscous, Reynolds, form-induced and total shear stresses are studied with comparisons made between distributions for hydraulically-smooth, transitionally-rough, and fully-rough boundaries. Measured streamwise turbulence intensities for all experiments peaked at a constant distance from the bed (z ++d + = 15) when elevation scale is adjusted using the zero-plane displacement d for the logarithmic velocity distribution. This collapse suggests that turbulence intensity distributions may be useful in assessing appropriate values of d for transitionally-rough and fully-rough boundaries. Form-induced normal and shear stresses above the roughness tops were found to collapse towards a common curve independent of roughness Reynolds number.
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This study is devoted to quantify the near-bed turbulence parameters in mobile-bed flows with bed-load transport. A reduction in near-bed velocity fluctuations due to the decrease of flow velocity relative to particle velocity of the transporting particles results in an excessive near-bed damping in Reynolds shear stress (RSS) distributions. The bed particles are associated with the momentum provided from the flow to maintain their motion overcoming the bed resistance. It leads to a reduction in RSS magnitude over the entire flow depth. In the logarithmic law, the von Karman coefficient decreases in presence of bed-load transport. The turbulent kinetic energy budget reveals that for the bed-load transport, the pressure energy diffusion rate near the bed changes sharply to a negative magnitude, implying a gain in turbulence production. According to the quadrant analysis, sweep events in mobile-bed flows are the principal mechanism of bed-load transport. The universal probability density functions for turbulence parameters given by Bose and Dey have been successfully applied in mobile-bed flows.
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