The scattering and radiations of linear oblique waves by multiple long horizontal circular cylinders submerged in water of finite depth are investigated using the multipole expansion method. Analytical expressions for the diffracted and radiated potentials are given as a linear combination of infinite multipoles. The unknown coefficients in the expressions are determined by using the addition theorem of the Bessel function and the cylinder boundary conditions. Also analytical expressions for wave forces, hydrodynamic coefficients and reflection and transmission coeffi-cients are derived. The present analytical solution is verified through the boundary element method and applied to investigate three different cases of the interaction of oblique waves with multiple submerged horizontal circular cylinders. The results show that the number of cylinders, the arrangement and spacing between cylinders play an important role in wave forces, hydrodynamic coefficients and reflection and transmission coefficients. Some interesting and important phenomena are ob-served in numerical experiments.
Based on the Preissmann implicit scheme for the one-dimensional Saint-Venant equation, the mathematical model for one-dimensional fiver networks and canal networks was developed and the key issues on the model were expatiated particularly in this article. This model applies the method of three-steps solution for chaunel-junction-channel to simulate the river networks, and the Gauss elimination method was used to calculate the sparse matrix. This model was applied to simulate the tree-type irrigation canal networks, complex looped channel networks and the Lower Columbia Slough networks. The results of water level and discharge agree with the data from the Adlul and field data. The model is proved to be robust for simulating unsteady flows in river networks with various degrees of complex structure. The calculated results show that this model is useful for engineering applications in complicated river networks. Future research was recommended to focus on setting up ecological numerical model of water quality in river networks and canal networks.
