Maximum run-up, breaking conditions and dynamical forces in the swash zone: a boundary value approach

On the basis of the approximate analytical solution for the nonlinear shallow water equations of Antuono and Brocchini [M. Antuono & M. Brocchini, The boundary value problem for the nonlinear shallow water equation, Stud. Appl. Maths, 119, 71–91 (2007).], we propose useful regression curves for the prediction of maximum run-up and dynamical forces in the swash zone on a frictionless, uniformly sloping beach. For the first time the dependence of the results on both the wave height and the wave steepness is analyzed in detail providing formulae able to describe a wide class of wave inputs. Finally, the regression formulae are validated through comparison with maximum run-up laws and breaking conditions already available in the literature, the present model results appearing to better account for nonlinear effects.