Equilibrium planform of pocket beaches behind breakwater gaps: On the shape of the equilibrium shoreline

Abstract

Bay beaches are common coastal landforms along the world’s coastlines and have frequently been used as equilibrium coastal systems to mitigate erosion problems and stabilize coasts. Throughout the literature, several formulae can be found to obtain the static equilibrium planform (SEP) of such beaches on the leeward sides of single protruding headland structures. However, equations used to define SEP behind breakwater gaps are rare and based on a limited number of studies, especially when the obliquity angle (β) is large. This paper proposes a new formula for modelling the SEP of bay beaches that includes cases with planform shapes characterized by large obliquity angles (β > 75°) for which the SEP is almost quasi-semicircular. The formula represents a general form of the parabolic bay shape equation (PBSE) with modified coefficients to alter the planform’s curvature to be quasi-semicircular, mimicking the behavior of such bays in nature. The coefficients are expressed as functions of both the obliquity angle (β) and the curvature-adjustment angle (𝝓�), which was determined based on field observations of the best-fitting SEP of 26 bay beaches with (β > 75°) along the coasts of Spain, Portugal and Brazil. Additionally, 32 beach cases characterized by smaller obliquity angles (β < 70°) were included in the derivation of the curvature adjustment angle, which was expressed as a function of (β). The model showed good results in modelling the SEP, with an RMSE of 0.90° obtained when estimating the planform’s curvature-adjustment angle (𝝓�) to obtain quasi-semicircular planform shapes for the prototype cases, confirming its utility as a valuable tool for engineering applications.