A logarithmic bottom boundary layer model for the unsteady and non-uniform swash flow

This paper presents a bottom boundary layer model for the unsteady and non-uniform flow in the swash zone, by extending the momentum integral method so as to include spatial gradients. The developed model is further incorporated into a hydrodynamic model based on the Nonlinear Shallow Water Equations. Two swash zone cases are examined to investigate the effect of the inclusion of spatial gradients. In the first of the two, boundary layer development under non-breaking periodic waves formulated by Carrier and Greenspan (1958) is investigated (wave-driven swash). Results show that the spatial gradients have the most pronounced effect in the lower swash, and in the region just seaward. In both these regions the spatial gradients enhance (diminish) onshore (offshore) bed shear stress, thus potentially contributing to onshore sediment transport under non-breaking waves. The second case investigated is the Kikkert et al. (2012) dam-break swash event (bore-driven swash). The model results are qualitatively and quantitatively accurate when compared against the laboratory measurements, and the velocities in the later backwash agree more closely with the measurements than those of Briganti et al. (2011). Results show that the inclusion of spatial gradients also favours onshore sediment transport in the lower swash. In addition, the bottom boundary layer is more fully developed in the uprush tip, resulting in smaller bed shear stress in the upper swash. The extended momentum integral method thus appears to capture more comprehensively the swash boundary layer, and the approach, therefore, offers a way forward in more accurate reproduction of swash dynamics in computational modelling.