Momentum Defect Superposition Model for Predicting Depth-Averaged Velocities in Trapezoidal Channels

Author

Matthew Ray Hagene, Southern Illinois University CarbondaleFollow

Date of Award

5-1-2011

Degree Name

Master of Science

Department

Civil Engineering

First Advisor

Wilkerson, Gregory

Abstract

An analytical model based on linear superposition of momentum defects is developed for predicting depth-averaged velocity distributions in trapezoidal and rectangular channels with submerged and unsubmerged rigid cylinders (i.e., simulated vegetation). The model is founded on wake theory and there is an existing model that is similar except for using linear superposition of velocity defects. The momentum defects and velocity defects supposition models both require a criterion for deciding when wakes created by the rigid cylinders will be considered completely dissipated (cutoff criterion). Comparing the momentum defects and velocity defects models required developing a new cutoff criterion that would have an equivalent effect when applied to either model. The chosen cutoff criterion considers a wake to be completely dissipated when u_max (the maximum defect caused by a cylinder) is less than or equal to 0.2 m/s. Predicted depth-averaged velocities from both models were compared to measured values. The predicted values differed from the measured values by less than 20% in general. It was concluded that the depth-averaged velocity predictions from the linear superposition of momentum defects model and the linear superposition of velocity defects model do not differ significantly and that the greatest advantage of the velocity defects model is that compared to the momentum defects model it is simpler to implement.