Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Complete list of metadata

Cited literature [96 references]  Display  Hide  Download
Contributor : Gaël RICHARD Connect in order to contact the contributor
Submitted on : Wednesday, June 27, 2018 - 4:44:48 PM
Last modification on : Monday, July 4, 2022 - 9:57:39 AM
Long-term archiving on: : Thursday, September 27, 2018 - 1:40:26 AM


Files produced by the author(s)


  • HAL Id : hal-01824889, version 1


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⟩



Record views


Files downloads