Swash flow properties with bottom resistance based on the method of characteristics

In the swash zone, an assessment of swash flow properties requires an understanding of swash depth and swash velocity, which can affect sediment movement, as well as the design of coastal structures. The method of characteristics provides a useful tool to model unsteady shallow water flows, such as dam-break flow, swash flow and tsunami run-up. In this paper, bottom resistance was incorporated into the nonlinear shallow water equations to extend the application of the method of characteristics to account for frictional effects in the swash zone. The new characteristic equations are solved by the specified time interval scheme. The bottom resistance has little influence on the seaward swash hydrodynamics (initial swash stage), e.g., water depth and flow velocity, while its influence becomes significant in the small water depth region near the swash front, which reduces the maximum run-up height. At a specified time and location, and comparing with a frictionless swash solution, the uprush flow velocity reduces due to the bottom resistance, while the flow velocity increases during the initial phase of the backwash owing to the earlier reversal time with the bottom resistance. However, the differences with the inviscid solution are small within the swash lens. Conversely, the maximum backwash velocity is reduced significantly as a result of the shorter duration of the backwash. Consistent with previous field observations, friction does not significantly alter the gradient of the water surface elevation and a seaward-dipping water surface elevation is observed during the majority of the swash process. The dominant effect of bottom resistance is to reduce the range of inundation, particularly with larger resistance coefficients. The incorporation of the bottom resistance extends the application of method of characteristics in the swash zone to more practical problems, particularly where run-up elevation is critically important, e.g. overtopping flows.