Equilibrium planform of pocket beaches behind breakwater gaps: On the location of the intersection point

Pocket beaches bounded by coastal structures are widely used as coastal systems that are in equilibrium for shoreline stabilization. Throughout the literature, several equations can be found to obtain the static equilibrium planform (SEP) of these embayed beaches, such as the parabolic bay shape equation (PBSE). The literature has already addressed some methodologies used to determine the location of the down-coast control point from which the parabolic shoreline is applicable for pocket beaches to the leeward side of a single headland structure. However, a methodology for locating this down-drift limit for double-curvature pocket beaches behind breakwater gaps is still lacking. This paper explores a methodology for locating this down-drift limit, hereafter called the intersection point (Pi), and investigates the role of the breakwater gap configuration as well as the directional wave climate close to the gap by employing 32 prototype beach cases along the Spanish coast. Moreover, an extensive series of numerical simulations using a spectral wave model was carried out to model the wave refraction-diffraction conditions on the leeward side of a breakwater gap under different wave conditions and various gap configurations. The results show the importance of the gap width and its orientation (θgap) with relation to the direction of the mean wave energy flux (θEF) at the gap as well as the ratio of the widths of the two parts of the bay beach that are affected by the breakwaters, denoted as the breakwater influence ratio (BIR), on the location of the intersection point (Pi). The results also indicated that a symmetrical pocket beach with a gap orientation (θgap) parallel to the θEF direction has an intersection point (Pi) around the mid-width point of the breakwater gap. On the other hand, the larger the difference angle (Δθgap) between θgap and θEF is, resulting in asymmetrical beach cases, the wider the eccentricity of the location of the intersection point (Pi) from the gap centerline towards the shallower landward breakwater of the gap is. New formulae were derived for calculating the angles used to locate the intersection point (Pi) from the two diffraction points of the gap as a function of the gap width, BIR and the offshore distances of the diffraction points. The model showed good results, with R2 = 0.9571 and an RMSE value of 0.9731° in estimating the location of the intersection point (Pi) in various prototype beach cases, confirming its utility for