Graduate Thesis Or Dissertation
 

Wave interaction with rubble mound structures

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  • The objective of this study is the development and verification of an analytical solution for an unsteady flow field partially occupied by a permeable structure. Flow is induced by a small amplitude incident wave train and the permeable structure may contain multilayered anisotropic but homogeneous material. The analytical solution developed for this project is based upon Lee's (1987) theory for a two-dimensional permeable structure with arbitrary geometry, which was applied to a seawall with toe protection and validated with large scale experiments. In the present study, the analytical solution is modified for application to a rubble mound breakwater structure. The existence of both waves and permeable media in the flow domain suggests that nonlinear losses within the structure and at the boundaries between different media are a significant problem. The random arrangement of the permeable media also precludes a precise description of the rigid boundaries of the flow inside structures. In view of these limitations and uncertainties, a solution to the problem is sought by treating the media as a locally homogeneous medium and by combining analytically precise deterministic forms of the equation of motion. Resistance forces in the permeable structure are modeled as inertia forces and form drag. Form drag is empirically nonlinear and is replaced by a linear drag term utilizing Lorentz's condition of equivalent work. Periodic non-convective motions can then be shown to be irrotational, ensuring the definition of a singlevalued velocity potential. In turn, the velocity potential satisfies a partial differential equation which reduces to the Laplace equation when the media are isotropic. A rubble mound breakwater usually contains inclined boundaries that make it mathematically unattractive. This difficulty can be overcome by partitioning the entire flow domain into a group of rectangular subdomains. An eigen-series representation of a damped wave propagating in each subdomain is then solved from the imposed boundary value problem, using a variable separation technique. The kinematic and dynamic boundary conditions on the boundary between any two adjacent subdomains and on the free surface are matched, while the kinematic boundary condition on any impermeable boundary is also satisfied. The solution in the subdo main with an open boundary at infinity satisfies Sommerfeld's (1949) radiation boundary condition. Solutions are expressed theoretically in terms of infinite series, with only a finite number of modal waves considered in actual computations. A Fortran program has been developed to facilitate these computations.
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