Abstract
To gain insight into the physical behaviour of 2D hydraulic models (mathematically formulated as a system of partial differential equations), the method of characteristics is used to analyse the propagation of physical meaningful disturbances. These disturbances propagate as wave fronts along bicharacteristics (rays) into the physical solution domain, while carrying the information from initial and boundary conditions. The method is applied to 2DH models for flow on a fixed and a 2DH two-layer model for turbidity currents in a reservoir. Introducing a point disturbance, circular shaped wave fronts develop related to water movement, and a star-shaped wave front related to disturbances in the mobile bed. A transversal wave front, related to vorticity, is formed in all models. An essential difference is shown in the propagation of the wave fronts for subcritical and supercritical flows. The characteristics have been used to define rules for imposing boundary conditions, and to find a stability condition for the layer 2D flow. The theory presented in this report is also applicable to other two-dimensional engineering problems, and is important for imposing boundary conditions and for using the 2D numerical solution methods.
Acknowledgements
This report has been written during my employment as a research assistant (AlO) in the Hydraulic and Geotechnical Engineering Division of the faculty of Civil Engineering of the Delft University of Technology. This study is carried out as part of a research project to sedimentation in reservoirs, a joint cooperation between Delft University of Technology and Delft Hydraulics, under supervision of Prof. Dr. M. de Vries (Delft University of Technology).
I am indebted to Prof. Dr. M. de Vries for his encouraging support and guidance and his critical reading. Special thanks are due to Dr. Z.B. Wang for his thorough and critical screening of the derivations in this report, and his indispensable comments.
I would also like to express my appreciation to Mr. E. Mosselman and Dr. H.]. de Vriend for providing me with helpful information and valuable suggestions.
