Investigation of Momentum Correction Factor in the Swash Flow

Abstract

Swash flows are commonly modeled using the nonlinear shallow water equations (NSWEs). In the derivation of the NSWEs, directly from depth-averaging the Navier–Stokes equations, a so-called momentum correction factor, β, emerges. In this study we present a numerical model of the NSWEs that includes β, which is allowed to vary in space and time, and feedback onto the flow. We apply this model to a swash flow, by making use of the vertical flow structure calculated by use of the log-law boundary layer and free flow region. We thereby examine its influence on the swash-flow predictions of a dam-break swash event described in the literature. The numerical results show that the momentum correction factor has a significant effect on the shoreline motion, and flow adjacent to the shoreline, which results in an overprediction of the shoreline with respect to the standard (β = 1, NSWE) approach. Given that consideration of β should yield a more complete description of the swash dynamics, the implication is that the log-law boundary layer model does not describe the flow structure in the swash tip region well. The implication of this is that to achieve accurate modeling at the flow uprush tip, at which point the largest bed shear stresses are typically exerted, a different submodel is required in that vicinity. Equally, it suggests that classical NSWEs also cannot describe the flow at the tip well, and that accurate prediction is achieved despite this inherent deficiency.