An Improved One-Line Evolution Formulation for the Dynamic Shoreline Planforms of Embayed Beaches

Abstract

In this paper, an improved one-line evolution formulation is proposed and derived for the dynamic shoreline planforms of embayed beaches. Although embayed sandy beaches can perform several functions, serving as leisure spots and areas of coastal protection, shoreline advances and retreats occur continuously as a result of many natural forces, such as winds, waves, currents, tides, etc. The one-line evolution formulation for dynamic shoreline planforms based on the polar coordinate can be adopted to simulate high-planform-curvature shorelines and achieve better stability and simplicity in comparison with other description coordinates. While the polar coordinate and rectangular control volume are adopted to derive the one-line evolution formulation for dynamic shoreline planforms, the difference between the radial direction of the polar coordinate and the normal direction of the shoreline segment may result in inaccurate predictions of shoreline movements. In this study, a correction coefficient, which can adjust the influence of these two misaligned directions, is derived and included in the one-line evolution formulation, which is based on the polar coordinate. Thus, by considering the correction coefficient, an improved one-line evolution formulation for dynamic shoreline planforms of crenulate-shaped bays is proposed in this paper. Some numerical examples are provided to verify the merits of the proposed improved one-line evolution formulation. Moreover, the proposed numerical approach is applied to simulate the dynamic movements of the shoreline in Taitung—the southeastern part of Taiwan—and the effectiveness of the proposed formulation in solving realistic engineering applications is evidently verified.