An approximate explicit analytical solution for the frictionless swash hydrodynamics with an improved seaward boundary condition

The classical Shen and Meyer (1963) analytical solution gives much shallow and asymmetric swash flows comparing with experimental observations. In this study, after considering an improved seaward boundary condition controlled by a parameter k proposed by Guard and Baldock (2007), a simple approximate analytical solution of the dam-break induced breaking bore propagation along the frictionless swash zone was deduced. The present analytical solution, though approximate since its validity is limited to the early stage of the swash evolution, is explicit allowing immediate and proper investigation of the swash hydrodynamics under the improved seaward boundary condition. After comparing with the implicit analytical solution by Pritchard et al. (2008), it is found that the present solution can be well applied to the entire swash process for relatively small k values and the uprush stage for all k values, which slightly overestimates the water depth and flow velocity during the backwash in the case of large k values. As parameter k increases, the present solution predicts increased mass and momentum fluxes entering into the swash zone, which is found to be ascribed to two specified reasons. One is the greater water depth and larger flow velocity near the original shoreline which leads to more water into the swash zone, and the other comes from the postponed flow reversal time which extends the entire uprush process. Comparison with the shock solution proposed by Antuono (2010) reveals that the shock induced and the present dam-break induced swashes are different in the initial incident conditions and the hydrodynamics during the swash process, ascribing to the different characteristic variable features in the calculation domain of the two solutions.

Automated summary

In this study, an improved analytical solution for studying swash hydrodynamics was deduced by considering a parameter k-controlled seaward boundary condition. The solution was found to be applicable to different stages of the swash process, but may slightly overestimate water depth and flow velocity in certain cases.