Computation of 3‐D Flow and Shear in Open Channels

Abstract

A mathematical modeling technique is presented which is capable of simulating various patterns of primary flow velocity distribution which may have the point of maximum velocity on or below the water surface. The simulated primary flow isovels are then used as a coordinate system in hydrodynamic analysis, to develop equations to compute corresponding distributions of shear stress and secondary flow. The mathematical models developed can be used to determine interactions among the primary flow velocity, shear stress and secondary flow velocity which all have a three‐dimensional distribution. The approach is essentially semi‐empirical which uses a measured or simulated distribution of primary flow velocity. It is designed to facilitate practical applications in studying various process in open channels, such as diffusion and dispersion of sediment, local scour and deposit, bank erosion, changes in channel geometry, aggradation and degradation of channel bed, which require three‐dimensional modelings. An application to a flow in a bend of a laboratory flume has shown that results of simulating the distributions of primary flow velocity and shear stress agree well with the measured data. Large discrepancies are found to exist between the computed and measured secondary flow velocities. However, it is still uncertain whether the discrepancies are entirely due to modeling and computational errors as the accuracy level of measured data is unknown.