Water waves approaching a beach undergo dramatic transformations, with the resulting flow dynamics being important for coastal transport of sediment and pollutants. We consider this situation using the non-linear shallow water equations, presenting both canonical and new solutions that are compared against data from large-scale laboratory experiments. Using the characteristic form of the equations, we show how breaking waves tend to create a uniform field of the forward-moving characteristic variable and how this results in a flow that mimics a dam break. We find good agreement between this solution and laboratory measurements of flow and solute transport, with exceptions in certain regions of x-t space that are discussed further. In cases where waves approach the beach at an oblique angle, we show how a new solution based on the characteristic variables agrees well with laboratory data. Together, these results suggest an underlying pattern to the seemingly complex flow due to waves on a beach, and the possibilities for improved predictions of coastal transport processes.

Refreshments will be served preceding the talk, starting at 2:45.