A Comparative Study of Wave Breaking Models in a High-Order Spectral Model

Abstract

We examine the implementation of two different wave breaking models into the nonlinear potential flow solver HOS-NWT. HOS-NWT is a computationally efficient, open source code that solves for surface elevation in a numerical wave tank using the High-Order Spectral (HOS) method [1]. The first model is a combination of a kinematic wave breaking onset criteria proposed by Barthelemey, et al. [2] and validated by Saket, et al. [3], and an energy dissipation mechanism proposed by Tian, et al. [4, 5]. The wave breaking onset parameter is based on the ratio of local energy flux velocity to the local crest velocity. Once breaking is initiated, an eddy viscosity parameter is estimated based on the pre-breaking local wave geometry, as described in [4, 5]. This eddy viscosity is then added as a diffusion term to the kinematic and dynamic free surface boundary conditions for the duration of wave breaking. Results implementing this wave breaking mechanism in HOS-NWT have shown that the model can successfully calculate the surface elevation and corresponding frequency spectra, as well as the energy dissipation associated with breaking waves [6–8]. The second model implemented to account for wave breaking in HOS-NWT is based on the method proposed by Chalikov, et al. [9–11]. This model defines wave breaking onset by the curvature of the water surface and defines the wave as broken if it exceeds a certain value. A diffusion term is added to the kinematic and dynamic free surface boundary conditions which dissipates energy based on the local curvature of the water surface, which is consequently not constant in space nor time. Calculations made using the two models are compared with large scale experimental measurements conducted at the Hydrodynamics, Energetics and Atmospheric Environment Lab (LHEEA) at Ecole Centrale de Nantes. Comparison of calculations with measurements suggest that both models are successful at predicting wave breaking onset and energy dissipation. However, the model proposed by Barthelemy, et al. [2] and Tian, et al. [4] can be applied without knowing anything about the breaking waves a priori, whereas the model proposed by Chalikov [9] requires tuning to specific conditions.