| Analytic models for the propagation of linear water waves over a trench or shoal of finite width and infinite length (2-D Step Model) and over an axisymmetric bathymetric anomaly (3-D Step Model) are developed. The models are valid in a region of uniform depth containing a bathymetric anomaly of uniform depth with gradual transitions in depth allowed as a series of uniform depth steps approximating linear or non-linear slopes. The velocity potential obtained determines the wave field in the domain.; The 2-D Step Model provides the complete wave field and, therefore, the reflection and transmission characteristics for depth anomalies of infinite length that are either symmetric or asymmetric. The 3-D Step Model determines the wave transformation caused by the processes of wave refraction, diffraction and reflection. Using the known velocity potential an energy flux approach is used to calculate the wave angle and reflected energy at large distances from the anomaly. The 3-D Step Model is joined with an analytic shoaling and refraction model (Analytic S/R Model) to extend the solution into the nearshore region. The Analytic S/R Model is employed to propagate the wave field up to the point of depth limited breaking. The breaking wave conditions are used to drive the longshore sediment transport and associated shoreline change using the Shoreline Change Model, which provides estimates of the equilibrium shoreline planform located landward of a bathymetric anomaly.; Comparisons of the 2-D Step Model to shallow water models developed in the study, previous studies, and a numerical model are made with good agreement demonstrated. The reflection coefficients found for symmetric and asymmetric trenches and shoals indicate multiple and no instances of complete transmission, respectively, with the solution independent of the incident wave direction for both cases.; Comparisons to a shallow water model, numerical models, and experimental data verify the results of the 3-D Step Model for several bathymetries, with the Analytic S/R Model verified by a numerical model for breaking wave conditions. Modeled equilibrium planforms landward of bathymetric anomalies indicate the importance of the longshore transport coefficients with either erosion or shoreline advancement possible for several cases presented. |
