Around 60% of global rivers do not form deltas, but relatively little attention has been given to the conditions at river mouths at which delta formation is prevented. Here we present an equation for predicting the spread of river-delivered sediments at coastlines subject to combined high energy waves and tidal ranges, for which delta formation is inhibited. This equation is validated against previous numerical modelling work on an idealised coast with a discharging river using Delft3D. The equation is derived from a mass-conserving bottom-evolution equation, reformulated to a partial differential equation, from which the analytical solution is determined using the method of Eigenfunction expansion.

The analytical approach is calibrated against the results of the Delft3D simulations, in order to determine values of two independent variables (downslope diffusion coefficient κ and input width B) controlling the shape of alongshore sediment distribution after a given time. This approach leads to only very small errors in determining alongshore sediment distribution when compared to the computationally expensive Delft3D simulations, and may be calculated in a fraction of the time.