Applicable sloping range and bottom smoothing treatment for σ-based modeling of wave propagation over rapidly varying topography

Accurate modeling of nonlinear wave propagation over mildly or rapidly varying topography is an important topic in costal/ocean engineering. This study examines the applicable sloping ranges and proposes a bottom smoothing treatment for the σ-based modeling framework. An efficient non-hydrostatic σ model is chosen to be validated against a series of experiments with various slopes from 1:20 to 1:∞. The measured and simulated free surface time series are compared and analyzed using both one- and two-dimensional short-time Fourier transform. The reflection rate and high harmonic generation including a recurrence behavior are characterized and discussed. Overall, the excellent agreement reveals the applicability of the σ-based model along with an appropriate 1:0.5 virtual slope to the wave problems with vertical (or extremely steep) bottom topography.