Analytical solutions of one-line model of shoreline change on the evolution of river delta on a coast bounded by solid boundaries

A river delta is a landform created when rivers empty their water and sediments into another body of water, such as an ocean, lake, or another river. This study proposes a new analytical solution for the one-line model of shoreline change by solving the nonhomogeneous linear ordinary partial differential equation. It describes river delta formation from the river sediment supply (point source) on a bounded coast, where the ends of the coast are fixed by solid boundaries. Furthermore, new analytical solutions are obtained by applying the property of linear superposition. These solutions describe the retreat of the river delta shoreline near the river mouth caused by the reduction of river sediment supply. They also outline the river delta shoreline recovery following the recovery of river sediment supply. A new analytical solution that describes shoreline evolution for an instantaneously shifting river mouth on the bounded coast is proposed by employing the same method. In addition, the resultant data is compared with the corresponding evolutions of the river delta shoreline on the coast without solid boundaries. Theoretical results indicate that river delta formation on the bounded coast is more rapid than on an unbounded coast. This can be attributed to the restriction of sediment loss by the solid boundaries. The boundary influence time of the solid boundary is defined as the time elapsed when solid boundaries interrupt the sediment transport and result in a significant difference of shoreline evolution compared to the coast without the solid boundaries. Its value in dimensionless form varies from 0 to 0.07, depending on the location of the river mouth, which acts as a point source. During the period of sediment reduction, the extent of retreat and the region of retreat near the river mouth are smaller and narrower than the case without solid boundaries. The deposition occurs on the side where the location of the river mouth channel is advancing, while erosion is observed on the other side. The results of this study were not verified with measured data. However, the derived solution would be a benchmark for numerical solutions and beneficial to the primary design stage, educational purposes, river delta, and river management authorities. � 2021 Elsevier Ltd