A two-dimensional velocity distribution model for gradually varied open channel flow using Poisson's equation

This dissertation presents, discusses, and validates a two-dimensional velocity and shear stress distribution model that can be used to analyze open channel flow in natural channels using traditional cross section data. The model is derived by combining a simplified form of the Reynolds equations for uniform flow through prismatic ducts with the Chezy formula from one-dimensional hydraulics. The result is a linear partial differential equation known as Poisson's equation that is relatively easy to solve for any cross section geometry. Because the model predicts two-dimensional velocity distributions assuming uniform flow at a cross section, it is referred to as the 2-D velocity distribution model.;The 2-D velocity distribution model is calibrated using familiar roughness coefficients such as Chezy's C and Manning's n. In addition to analyzing uniform flows, the model can be combined with the one-dimensional gradually varied flow equation to produce water surface profiles. The individual velocity distributions generated at each cross section can then be interpolated to create a pseudo three-dimensional flow field of a channel reach.;The validity of the 2-D velocity distribution model was investigated using data collected from streams in the western United States and by comparing its predictions to those obtained using the Manning formula. The average standard error of the model's velocity distribution predictions at stream cross sections was about 33%. Comparisons between the 2-D velocity distribution model and the Manning formula demonstrated a strong correlation between the two techniques for determining stage-discharge relationships. Using the same roughness coefficients, their agreement varied from 85 to 100% depending on cross section geometry and depth of flow. Composite channel roughness comparisons revealed excellent agreement between the model and the Manning formula when Lotter's method was used to calculate an equivalent channel roughness coefficient.;The 2-D velocity distribution model can be used to reasonably approximate two-dimensional velocity and shear stress distributions at a cross section in natural channels. Applications of the model include improved erosion and sedimentation calculations, as well as a systematic method for determining equivalent roughness coefficients for compound and composite roughness channels.