The run-up of nonbreaking and breaking solitary waves

Abstract The run-up of nonbreaking and breaking solitary waves on plane impermeable beaches is investigated with a Lagrangian finite-element Boussinesq wave model. Wave breaking is parameterized with an artificial viscosity (diffusion) term in the momentum equation, and bottom friction is modelled with a term quadratic in the horizontal fluid velocity. Comparisons are presented with laboratory data of maximum run-up, shoreline motion, and spatial profiles of near-shore free-surface elevation for both steep (20°) and gradual (2.88°) slopes. For the steep slope, only waves which do not break on run-up are considered, and excellent agreement is obtained with the laboratory data. For the gradual slope, wave shoaling, breaking, bore formation and subsequent collapse at the shoreline are predicted well by the model, although the breaking algorithm does not attempt to model the details of the turbulent flow in the breaking region. The backwash bore is also modelled reasonably well, although it persists longer in the numerical computations than in the laboratory data. It is shown that the inclusion of nonhydrostatic effects reduces the tendency of waves to break and improves the agreement of the numerical results with the laboratory run-up data. This allows higher amplitude waves to be modelled and larger propagation distances to be treated without the need to limit the wave steepness with artificial dissipation.