Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach

Abstract

The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes nonoverturning waves. Including the impacts of wave breaking dissipation is however possible by implementing a wave breaking initiation criterion and dissipation mechanism. Three criteria from the literature, including a geometric, kinematic, and dynamic-type criterion, are tested to determine the optimal criterion predicting the onset of wave breaking. Three wave breaking energy dissipation methods are also tested: the first two are based on the analogy of a breaking wave with a hydraulic jump, and the third one applies an eddy viscosity dissipative term. Numerical simulations are performed using combinations of the three breaking onset criteria and three dissipation methods. The simulation results are compared to observations from four laboratory experiments of regular and irregular waves breaking over a submerged bar, irregular waves breaking on a beach, and irregular waves breaking over a submerged slope. The different breaking approaches provide similar results after proper calibration. The wave transformation observed in the experiments is reproduced well, with better results for the case of regular waves than irregular waves. Moreover, the wave statistics and wave spectra are predicted well in general, and in particular for regular waves. Some differences are observed for irregular wave cases, in particular in the low-frequency range. This is attributed to incomplete absorption of the long waves in the numerical model. Otherwise, the wave spectra in the range [0.5fp, 5fp] are reproduced well, before, inside, and after the breaking zone for the three irregular wave experiments.

Wave–bottom interaction and extreme wave statistics due to shoaling and de-shoaling of irregular long-crested wave trains over steep seabed changes

“…The free-surface boundary conditions (2.3) and (2.4) are expressed as functions of free-surface variables η(x, t) andφ(x, t) ≡ φ(x, z = η(x, t), t), as (Zakharov 1968) In whispers3D, the DtN problem is solved by using a spectral approach in the vertical direction, following Tian & Sato (2008) and Yates & Benoit (2015). This code has been validated for numerous conditions (see Raoult, Benoit & Yates 2016;Simon et al 2019;Zhang et al 2019), showing excellent performance for the prediction of wave propagation together with acceptable computational burden. The modelling approach of whispers3D has been presented in Yates & Benoit (2015) and Raoult et al (2016) and is briefly recalled here.…”

“…This code has been validated for numerous conditions (see Raoult, Benoit & Yates 2016; Simon et al. 2019; Zhang et al. 2019), showing excellent performance for the prediction of wave propagation together with acceptable computational burden.…”

Apports de modèles complètement non-linéaires et dispersifs pour la simulation déterministe de la dynamique des vagues en zone côtière

“…surface libre et la vitesse horizontale), et (iii) de la distribution statistique des hauteurs de vagues, y compris les vagues extrêmes, pour certaines dépassant le critère H > 2Hs, habituellement considéré pour identifier les vagues scélérates. Récemment, le code a été enrichi de modèles permettant de représenter le déferlement avec plusieurs critères de déferlement et modèles de dissipation, implémentés et validés pour des vagues régulières ou irrégulières (PAPOUTSELLIS et al 2019 ;SIMON et al, 2019).…”

Foreword to the special issue on nonlinear waves over variable bathymetry

“…The present special issue contains eight papers in total: three papers applying advanced, potential theory-based methods to wave problems involving complicated, uneven seabeds (Athanassoulis et al 2019; Touboul and Belibassakis 2019; Zhao et al 2019) 2 ; a paper exploiting a fully nonlinear potential flow solver to model wave breaking by means of boundary dissipation (Simon et al 2019); two papers investigating how simplified model equations can be best adapted to varying bathymetry conditions (Lalli et al 2019;Yu 2019); a paper examining the effect of wind forcing on modulational instability (Grimshaw 2019); and another one using the Navier-Stokes equations, thus being capable of producing reliable results for complicated nonlinear wave-seabed interactions, including rotational waveinduced currents (Gallerano et al 2019). More specifically:…”

“…Their conclusion is that the proposed generalized Green's law has an overall good performance when complex bathymetries are considered, except for small areas near seabed locations where the diffraction is intense. Simon et al (2019) are concerned with the modelling of wave-breaking onset and dissipation, in the context of a fully nonlinear and dispersive potential flow model. Nonlinear wave evolution is described by the Hamiltonian formulation treated with a spectral representation of the vertical structure of wave flow, using Chebyshev polynomials.…”