A new model of shoaling and breaking waves: One-dimensional solitary wave on a mild sloping beach - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2018

A new model of shoaling and breaking waves: One-dimensional solitary wave on a mild sloping beach

Abstract

We present a new approach to model coastal waves in the shoaling and surf zones. The model can be described as a depth-averaged large-eddy simulation model with a cutoff in the inertial subrange. The large-scale turbulence is explicitly resolved through an extra variable called enstrophy while the small-scale turbulence is modelled with a turbulent viscosity hypothesis. The equations are derived by averaging the mass, momentum and kinetic energy equations assuming a shallow water flow. The model is fully nonlinear and has the same dispersive properties as the Green-Naghdi equations. It is validated by numerical tests and by comparison with experimental results of the literature on the propagation of a one-dimensional solitary wave over a mild sloping beach. The wave breaking is characterized by a sudden increase of the enstrophy which allows us to propose a breaking criterion based on the new concept of virtual enstrophy. The model features three empirical parameters. The first one governs the turbulent dissipation and was found to be a constant. The eddy viscosity is determined by a turbulent Reynolds number depending only on the bottom slope. The third parameter defines the breaking criterion and depends only on the wave initial nonlinearity. These dependences give a predictive character to the model which is suitable for further developments.
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Dates and versions

hal-01824889 , version 1 (27-06-2018)

Identifiers

  • HAL Id : hal-01824889 , version 1

Cite

Maria Kazakova, Gaël Loïc Richard. A new model of shoaling and breaking waves: One-dimensional solitary wave on a mild sloping beach. 2018. ⟨hal-01824889⟩
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