Research papersModelling shoreline evolution in the vicinity of a groyne and a river

•The subject of the paper is shoreline evolution in the vicinity of a river mouth.•New analytical solutions are derived.•Solutions include littoral drift, groyne influence and inlet sediment supply/loss.•Solutions are extended to allow time varying waves and sediment supply/loss.•A practical example application of the new solution is provided.

Analytical solutions to the equations governing shoreline evolution are well-known and have value both as pedagogical tools and for conceptual design. Nevertheless, solutions have been restricted to a fairly narrow class of conditions with limited applicability to real-life situations. We present a new analytical solution for a widely encountered situation where a groyne is constructed close to a river to control sediment movement. The solution, which employs Laplace transforms, has the advantage that a solution for time-varying conditions may be constructed from the solution for constant conditions by means of the Heaviside procedure. Solutions are presented for various combinations of wave conditions and sediment supply/removal by the river. An innovation introduced in this work is the capability to provide an analytical assessment of the accretion or erosion caused near the groyne due to its proximity to the river which may act either as a source or a sink of sediment material.