Beaches in a semi-insulated compartment: Engineering tools from the diffusion theory

Beaches can serve as a valuable asset to any community, which can gain a massive source of income from them; in fact, beach tourism is ever more frequently the essential target of countries, aimed at attracting foreign investment or exchange. In this frame, prediction of coastal evolution at large scales is very important for coastal management and first conceptual design. Management strategies, almost at the early stages of the projects, may likely involve numerical simulations, but they can be extremely laborious, computing demanding and intensely time-consuming especially when involving either wider coastal domain or longer time scales that basically encompasses the majority of coastal projects by now. Analytical solutions of the Diffusion Shoreline Equation (DSE) can be a valid alternative. In these frames, given the surprisingly good predictive capabilities, they can isolate essential features of the processes, making them more readily comprehended, and can avoid cumulative errors associated with the accuracy of computational time-stepping models. Nevertheless, the rather complex mathematical form makes their use extremely challenging and confines them in the realm of high mathematics. Ciccaglione et al. (2023) provided analytical solutions of the DSE for finite beaches bounded by outcrops of whatever length (bypassing or non-bypassing groin compartments). Differently from the other studies, the authors checked the applicability range of the solutions through the comparison with reliable numerical models; furthermore, using curve fitting analysis simple design tools were suggested to aid engineers in the practical applications. In this paper, a deep focus is given on the case of a bypassing groin compartment, and easy-to-use formulae are given to assess the lifetime of beach fill projects. A simple semi-theoretical solution is also given for the case of a compartment bounded by a very short groin, by introducing a “convective term” modelled via a Heavy-side function, H(x). The practical usefulness of this solution is proved through an application to the evolution of a real beach along Italy’s Adriatic coast.