A theoretical study of plunging breakers and their run-up

Breaking oscillatory waves of the plunging type and their run-up are studied theoretically, using the nonlinear, shallow-water wave equations which are solved by the method of characteristics. Backwash velocities are included in the numerical scheme. The computational results, up to the wave breaking point, agree reasonably well with experimental data for waves on a 1/7.12 slope but there is poorer agreement for a 1/9.80 slope. An expression is presented for estimating the maximum frictional run-up on a dry beach. Results obtained from the new expression are reasonably close to the experimental curve for a rough beach sloping at 1/7.12. © 1981