A new approach to analytical modelling of groyne fields

Analytical and computational techniques for finding solutions to the equations describing shoreline evolution are widely known and the advantages and disadvantages of both are well documented. Initial analytical solutions to the 1-line models were restricted to constant wave conditions and simple beach/structure configurations. Recent developments in analytical treatments have allowed solutions to be found for an arbitrary sequence of wave conditions, but again for simple configurations. Here, we propose a method of linking several analytical solutions together in order to describe the unsteady evolution of a beach within a groyne field, allowing for both permability of the groynes and by-passing. The method relies on specifying boundary conditions in each groyne cell that mimic the transmission and by-passing of sediment. The conditions are generalisations of boundary conditions that are well-known. Solutions for groyne fields on straight and convex shorelines are presented to illustrate the method for constant and time varying wave conditions. •New analytical solutions are derived for extended groyne fields.•Solutions are constructed from existing solutions and novel internal boundary conditions.•Solutions include littoral drift, groyne by-passing and groyne permeability.•Solutions are extended to allow time varying waves and arbitrary initial beach shape.•Practical example applications of the new solution are provided.