Potential shoreline changes induced by three-dimensional bathymetric anomalies with gradual transitions in depth

Abstract

The development of an analytic model for nearshore wave propagation and shoreline change shoreward of a bathymetric anomaly is presented. The three-dimensional (3-D) Step Model (Bender, C.J., Dean, R.G., 2003. Wave transformation by axisymmetric 3-dimensional bathymetric anomalies with gradual transitions in depth. In Review: Coastal Engineering.) propagates a linear wave field in a region of uniform depth over an axisymmetric bathymetric anomaly to a region representing the nearshore zone. The bathymetric anomaly is represented by a series of steps, which can approximate uniform or nonuniform slopes. This paper presents the development and application of an approximate shallow water Analytic Shoaling and Refraction Method (Analytic S/R Model), which establishes the breaking wave height and angle for arbitrary nearshore slopes, thus extending the 3-D Step Model to the nearshore region where the depth is nonuniform. The 3-D Step Model determines the wave transformation caused by the processes of wave refraction, diffraction, and reflection. The wave heights and directions for transects located shoreward of the bathymetric anomaly are combined with the Analytic S/R Model to determine the wave propagation in a nearshore zone of arbitrary slope. Employing the Shoreline Change Model calculates the longshore transport and shoreline evolution for the nearshore (shoaled and refracted) wave field that occurs shoreward of the anomaly. Through the methods developed in this paper, the wave transformation, nearshore shoaling and refraction, longshore transport, and shoreline evolution induced by a 3-D bathymetric anomaly with gradual transitions in depth are investigated. Comparisons of the analytic nearshore shoaling model with a numerical model verify the results for several bathymetries including both pits and shoals. The analytic shoreline change model predicts shoreline response for areas shoreward of bathymetric anomalies. Comparison to the laboratory experiment of Horikawa et al. (Horikawa, K., Sasaki, T. and Sakuramoto, H., 1977. Mathematical and laboratory models of shoreline change due to dredged holes. Journal of the Faculty of Engineering, The University of Tokyo. XXXIV, No. 1, pp. 49–57) indicates the Shoreline Change model is able to predict the equilibrium planform shoreward of a pit when the transport caused by the gradient in breaking wave height is included. The results demonstrate the importance of the longshore transport term driven by the gradient in breaking wave height.