Analytical solutions of one-line model for shoreline change near coastal structures

Analytical solutions provide a simple and economical means of quickly estimating qualitative and quantitative responses of the shoreline to a wide range of environmental and engineering conditions. This paper presents analytical solutions for shoreline evolution in the vicinity of coastal structures, including detached breakwaters, seawalls, and jetties with and without wave diffraction. The solution for a detached breakwater illustrates the growth of a salient with time behind the breakwater and the associated initial shoreline retreat at locations across from the breakwater tips. A simple solution describing flanking of a seawall is obtained by using two different solution areas where the longshore sand transport rate and breaking-wave angle vary. A similar technique is used to model diffraction downdrift of a groin or jetty by allowing the wave angle to vary with the distance alongshore according to a specified function or by employing a large number of solution areas. Cases are also presented for the accumulation updrift a groin and the shoreline response in a groin compartment with a breaking wave angle that varies sinusoidally in time. A solution for a single groin illustrates the impact of bypassing on the updrift accumulation.