Efficient two-layer non-hydrostatic wave model with accurate dispersive behaviour

Abstract

A 2-layer non-hydrostatic model with improved dispersive behaviour is presented. Due to the assumption of a constant non-hydrostatic pressure distribution in the lower layer, the dispersive behaviour is improved without much additional computational time. A comparison with linear wave theory showed that this 2-layer model gives a better result for the dispersion relation and shoaling of waves in intermediate water. This means that the 2layer model is applicable in shallow and intermediate water depths (up to relative depths kh equals 4), whereas the 1-layer model is only applicable in shallow water depths (kh smaller than 1). Three laboratory experiments, including a fringing reef and a barred beach, were used to validate the presented mode for different hydrodynamic conditions. Based on these results, it can be concluded that the 2-layer model can be applied to accurately simulate the bulk wave height and spectral properties. The low frequency wave height, the setup and in particular the second order statistics contain more scatter, but the model accurately captured the general trend. Furthermore, the model showed good results for complex bathymetries in shallow to intermediate water.

A Model-Derived Empirical Formulation for Wave Run-Up on Naturally Sloping Beaches

“…The empirical relations presented in this paper were derived from many 1D XBeach-NH+ model runs [18], in which a wide range of offshore boundary conditions and crossshore geometries were simulated. Time series of vertical run-up were extracted from the results, and from these the mean set-up (z mean ), and the incident (S inc ) and infragravity (S IG ) components were computed.…”

“…The profile in the surf zone is schematized with a Dean profile [20] up to a depth of 4 times the offshore wave height. Beyond the surf zone, the bathymetry gradually drops to a depth where n (C/C g ) equals 0.8 [18]. The cross-shore grid resolution varies along the profile, such that individual waves are covered by approximately 80 grid cells.…”

“…Vertical run-up time series z t were obtained from a run-up gauge in the model which tracks the most landward wet point. The threshold water depth for determining whether a grid cell is wet was set to 0.01 m. Tests with this parameter did not show strong sensitivity to the results in the range between 0.01 and 0.05 m. The maximum breaker steepness was set to 0.6, as recommended by [18].…”

“…In the present approach study, we apply the XBeach-NH+ model [18] which is a quasi-two-layer dispersive model which resolves both the incident and infragravity waves up to a relative depth kh of 4. This model has shown good skill in predicting the wave hydrodynamics in field conditions [6] and wave run-up in laboratory conditions [7].…”

Modeling the Morphodynamics of Coastal Responses to Extreme Events: What Shape Are We In?

“…Wave-resolving models. One solution to the difficulty in parameterizing wave behavior in shallow water is to resort to wave-resolving models such as MITgcm, TRIM, SUNTANS, SWASH, CROCO, NHWAVE, FUNWAVE, Celeris, and XBeach-NH+ (Marshall et al 1997, Casulli 1999, Fringer et al 2006, Zijlema et al 2011, Debreu et al 2012, Ma et al 2014, Malej et al 2015, Tavakkol & Lynett 2017, and de Ridder et al 2021, which are capable of skillfully simulating the shapes and orbital motions of nonlinear waves (e.g., Tissier et al 2011, Smit et al 2014) and, critically, can resolve water-level variations associated with setup and swash. Although most wave-resolving models lack sediment-transport formulations and are still too computationally expensive to simulate regional-scale nearshore morphodynamics, we anticipate that this will change, and that wave-resolving models will be improved to incorporate breaking-induced turbulence, be coupled with sediment-transport formulae (e.g., van der A et al 2013van der A et al , Fringer et al 2019, and become more common components of coastal morphodynamic models.…”