a1 Department of Mathematics, University of Strathclyde, 26 Richmond St, Glasgow G1 1XH, UK email@example.com
a2 Department of Civil Engineering, University of Queensland, St Lucia, Queensland 4072, Australia
We use a hodograph transformation and a boundary integral method to derive a new analytical solution to the shallow-water equations describing bore-generated run-up on a plane beach. This analytical solution differs from the classical Shen–Meyer runup solution in giving significantly deeper and less asymmetric swash flows, and also by predicting the inception of a secondary bore in both the backwash and the uprush in long surf. We suggest that this solution provides a significantly improved model for flows including swash events and the run-up following breaking tsunamis.
(Received March 04 2008)
(Revised June 09 2008)