Influence of Swash Dynamics and Wave Spectral Structure on Beach Cusp Geometry

Beach cusp geometry arises from coupled hydrodynamic and morphodynamic feedback in the swash zone. This study used the numerical model XBeach in nonhydrostatic mode to examine cusp development on an idealized sandy beach forced by monochromatic, bichromatic, and band-limited irregular waves. Simulations systematically varied foreshore slope (tan β = 0.05–0.15), wave period (8–12 s), and wave height (0.4–0.8 m), while grouped and irregular cases isolated the effects of infragravity modulation and spectral bandwidth. Under monochromatic forcing, cusp spacing increased primarily with wave period and foreshore slope, whereas wave height played a secondary role. Cusp spacing scaled strongly with horizontal swash excursion, supporting self-organization. Grouped and band-limited forcing increased shoreline excursion but weakened the direct proportionality between cusp spacing and swash excursion, indicating the temporal organization of forcing modulated pattern evolution. Across monochromatic, bichromatic, and irregular cases, spectral diagnostics did not show dispersion-aligned energy consistent with edge-wave forcing. The results support the interpretation of beach cusps as predominantly swash-driven, self-organized features whose geometry is controlled by slope and incident-wave timescale and modulated by spectral structure.