Wave breaking onset and dissipation in a fully non-linear, staggered grid Boussinesq model
Date
2023
Authors
Journal Title
Journal ISSN
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Publisher
University of Delaware
Abstract
This research considers the pre- and post-breaking behavior of weakly-nonlinear (WNL) and fully-nonlinear (FNL) Boussinesq-type (BTE) models. We consider two primary questions: • 1. Is the FNL model capable of accurately reproducing shoaling behavior and esti- mates of parameters needed to describe the onset of breaking? • 2. How can the description of breaking be improved in order to accurately reproduce CFD calculations? ☐ It is clear from prior results that linear, KdV or WNL models do not reproduce shoaling behavior for waves close to breaking. Although previous results (for example, Wei et al., 1995) have shown accurate results for FNL model shoaling of solitary waves, it is not a foregone conclusion that this robustness would extend to shorter wavelengths. We address this question by examining wave crest and velocity field properties for a range of wave conditions, in comparison to either CFD calculations based on an LES/VOF model (Derakhti and Kirby, 2014) or a boundary element method potential flow solver (Grilli and Subramanya, 1996). ☐ Based on our tests, both the FUNWAVE 1-centered grid scheme (Wei and Kirby, 1995) and FUNWAVE-TVD (Shi et al., 2012) are shown to have deficiencies in accu- rately reproducing wave shoaling up to the breaking point for steep regular waves (in the first case) and solitary waves (in the second). We have successfully addressed this issue by employing a finite difference scheme using a staggered grid, which greatly en- hances the FNL Boussinesq numerical model and ensures precise numerical calculation of dispersion effects and shoaling. ☐ Due to their typical underlying assumption of irrotational flow, BTE models employ breaking closure models to identify the onset of breaking and calculate the dissipation resulting from breaking. Breaking onset in BTE models is usually defined using geometric criteria, while the dissipation of energy after breaking is parameter- ized using 0-equation models for the eddy viscosity based on empirically determined geometric criteria (Kennedy et al., 2000). We show that these simple representations significantly over-predict the decay of wave height immediately after breaking onset. ☐ We address these problems by (i) implementing the B-criterion, which offers a more robust kinematic threshold for identifying the onset of breaking. This criterion was initially proposed by Barth ́elemy et al. (2018) for deep and intermediate depths and subsequently validated by Derakhti et al. (2020) for all depths. (ii) For the dissipation of energy due to breaking we use a revised model based on a 1-equation closure for turbulent kinetic energy (TKE), first suggested by Nwogu (1996). Finally, we obtain a parameterization of the TKE for use in determining the eddy viscosity without the use of the closure model.
Description
Keywords
Boussinesq models, Nonlinear waves, Surface wave modeling, Water waves, Wave breaking