Ciccaglione, Margherita Carmen (2022) On the diffusion theory of shoreline evolution. [Tesi di dottorato]

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As known, coastal erosion phenomenon vastly varies over either the space or the time scale. Short-term coastal erosion (on the time scale of hours and days) due to its inherently reversibility, cannot be considered as a “real coastal erosion”; by contrast, coastal retreatment is intended in a “structural way” and only long-term processes may have permanent effects on coastal evolution in this regard. Without a proper grasp of these processes, shoreline evolution and outcomes of coastal structures may not be anticipated accurately. The ever-growing need to calculate shoreline change over long spatial extents and time frames, has led to a wide use of both analytical and numerical (one-line shoreline response) models, based on the one-line contour theory (Pelnard-Considere, 1956), which reduces, under certain hypotheses, to the diffusion equation. The common thread of present Ph.D. thesis is grasping if, and in what measure, the shoreline diffusion equation could be able to provide theoretical guidance, also useful under the practical point of view, regarding the long-term evolution of sandy coasts. In fact, the analysis of diffusion equation reveals peculiar aspects in coastal evolution also with respect to the long term impact of hard structures. The work is organized to cope with different innovative aspects of the research theme, which have never been deepened by the published research in this field, and namely: (1) the evolution of a stretch of coast of finite length bounded by solid boundary, for which a complete analytical model has been developed. The proposed model provides a clearer view on the limits of the diffusion approach on this problem. (2) The effect of a time-varying diffusivity on long-term shoreline evolution. This aspects regards the theoretical foundations of the “equivalent wave” concept, frequently used in the practical coastal engineering. (3) The organic introduction to the effect of a negative diffusivity on long-term evolution of sandy coasts, and the original interpretation of the effects of a detached breakwater on shoreline change are then studied. In fact, under an intriguing perspective, but not sufficiently deepened, at all, it is assumed that the positioning of a transmissive breakwater is nothing but the introduction of a negative diffusivity into a restricted area of the coast. (4) A more stringent relationship between wave crests and equilibrium shore profile, which demonstrates that the equilibrium position of shoreline does not corresponds to the wave fronts. The theoretical interpretation has been found through the diffusion approach. The research has been carried out either via theoretical approach, searching for analytical solution of practical interest of the heat equation, or via numerical approach, using the numerical one-contour line model GENESIS (Hanson and Kraus, 1989). Moreover, the analysis regarding the “diffusion aspects” (2) and (3) are supported by shoreline evolution data of Molise coast, relative to a long-term study between 1954 and 2016, which allowed a further comprehension of diffusion problems and peculiar features of coastal evolution. Conversely, the methodology behind (4) has been validated on a small pocket beach within the Bagnoli bay (NA).

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