This article provides closed form solutions of the Diffusion Equation (DE) for beaches of finite length bounded by outcrops; the method employed relies on the sum of two Sturm-Liouville Boundary Value Problems, which allow accounting for the effects of wave angle. From the general solution, three situations of engineering interest were extrapolated and discussed in detail. The first corresponds to a stretch of coast “pinned” at the extremes; the second refers to an “insulated” beach bounded by groins of infinite length and the third corresponds to a groin compartment bypassed at one end. All those solutions were previously known in the field of thermodynamics, but they are here derived systematically from a general Boundary Value Problem (BVP). A detailed comparison with the software GENESIS is carried out to establish the limits of application with increasing wave angles. The effects of the presence of outcrops is studied comparing the solutions for finite beaches with those proposed in the literature under the hypothesis of infinite shoreline (open coast). It is shown that the new approach can be particularly useful in the case of beach nourishments placed asymmetrically to the cell centre. For application purposes, approximate solutions are given, based on curve fitting, to calculate the remaining value of sediments in a beach fill of rectangular shape.
On the evolution of beaches of finite length / Ciccaglione, M. C.; Buccino, M.; Calabrese, M.. - In: CONTINENTAL SHELF RESEARCH. - ISSN 0278-4343. - 259:(2023), p. 104990. [10.1016/j.csr.2023.104990]
On the evolution of beaches of finite length
Ciccaglione M. C.;Buccino M.
;Calabrese M.
2023
Abstract
This article provides closed form solutions of the Diffusion Equation (DE) for beaches of finite length bounded by outcrops; the method employed relies on the sum of two Sturm-Liouville Boundary Value Problems, which allow accounting for the effects of wave angle. From the general solution, three situations of engineering interest were extrapolated and discussed in detail. The first corresponds to a stretch of coast “pinned” at the extremes; the second refers to an “insulated” beach bounded by groins of infinite length and the third corresponds to a groin compartment bypassed at one end. All those solutions were previously known in the field of thermodynamics, but they are here derived systematically from a general Boundary Value Problem (BVP). A detailed comparison with the software GENESIS is carried out to establish the limits of application with increasing wave angles. The effects of the presence of outcrops is studied comparing the solutions for finite beaches with those proposed in the literature under the hypothesis of infinite shoreline (open coast). It is shown that the new approach can be particularly useful in the case of beach nourishments placed asymmetrically to the cell centre. For application purposes, approximate solutions are given, based on curve fitting, to calculate the remaining value of sediments in a beach fill of rectangular shape.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
