Formation and evolution of beach cusps

Beach cusps are swash zone morphological patterns that have been of interest to many scientists and engineers. This study aims to improve understanding of the formation and long-term evolution of beach cusps by numerical simulation using a 2D process-based morphodynamic model, solving the coupled NLSW equations and sediment conservation equation simultaneously. A numerical implementation is applied building on the model of Dodd et al. (2008), which succeeds in simulating the occurrence of beach cusps. The numerical scheme improves the accuracy and stability of the swash zone computation. Results from a comparison between different numerical implementations concludes that the most suitable numerical scheme is the Roe-averaged scheme of Castro Diaz et al. (2008) with Minmod flux-limiter using the Harten and Hyman (1983) entropy fix method and the Hubbard and Dodd (2002) approach for the shoreline boundary condition. Before simulating the 2D beach cusps, the sensitivity of the model parameters and two different types of incoming waves are tested in the ID bed change. The sensitivity test results show that there is a convergence of the results when the minimum computational depth (dtol) ≤ 1 mm. Also the relationship between the bed profile and beach cusp parameters is that a greater maximum tip position (xs,max) is achieved, and more erosion in the tip region occurs when the bed friction coefficient (ƒw), the hydraulic conductivity (K), and dtol are smaller. On the other hand, the effect of scaling the sediment transport coefficient (A) is to scale the rate of change of the bed level, and appears not to lead to qualitative differences. Moreover, the incoming sine wave creates three components of 1D beach profile (long-shore bar, trough, and swash berm) in the computational domain, while the incoming sawtooth wave creates a wider equivalent region, because of wave simply breaking farther offshore. The 2D simulations give approximately the same beach cusp formation as those of Dodd et al. (2008); however, the geometrical parameters (ƒ) from the self-organisation theory are still high when compared with previous field observation and numerical simulations. The evolution of the beach cusps is investigated by Fourier and global analyses (Garnier et al., 2006), and can be divided into three stages: 1D development in the cross-shore profile, 2D small cusp spacing pattern, and 2D final bigger cusp spacing pattern, caused by the coalescing of two small bays and subsequent rearrangement to an equal spacing. However, an unphysical behaviour is found during cusp evolution, which is the reversing behaviour between horn and embayment. It appears that this reversible behaviour is caused by deposition at the embayment head, created from high infiltration and the usage of the velocity-only type of sediment transport equation in the model