The wavefront shift method for bay beaches

Abstract

Bay beaches, sheltered by one or more headlands, are predominant physiographic features along oceanic and sea coasts. Their distinctive planform is created through wave sheltering caused by diffraction, along with refraction wherever the indentation of the bay is large. The asymptotic scenario entailing no littoral drift along the bay is known as “static equilibrium”, and the shoreline contour associated with this long-term stable state is denoted as the Static Equilibrium Planform (SEP). SEP prediction is a crucial concept for engineering applications, as it serves to either check for the status of existing beaches or address erosion issues via headland control. The practical impact of this topic is reflected in the remarkable body of available literature. This article discusses a new SEP predictor, which focuses on wave diffraction as the primary driver shaping the bay. The approach, denoted as the Wavefront Shift Method (WSM), involves translating the diffracted wavefronts along the crestline of the incident waves. Diffracted wavefronts are obtained numerically by propagating regular waves with a Boussinesq model. Unlike other predictors, e.g. the parabolic equation, WSM does not rely on a mathematical formula established a priori; moreover, it features a clear connection to the physics of beach evolution. In 2021 the authors first introduced WSM for single-headland bays as an empirical result from their numerical investigation. This paper provides the method with a theoretical framework and extends it to include bays sheltered by two headlands. This extension is achieved by exploiting the Fraunhofer theory for the diffraction of light. The comparison with 20 natural bays along the Mediterranean coast indicates that WSM is a well-performing, easy-to-use approach with the potential to reduce, in some situations, the degree of subjectivism and complexity of the existing methods.