Nonlinear Shallow Water Theories for Coastal Waves

Ocean waves entering the near-shore zone undergo nonlinear and dispersive processes. This paper reviews nonlinear models, focusing on the so-called Serre equations. Techniques to overcome their limitations with respect to the phase speed are presented. Nonlinear behaviours are compared with theoretical results concerning the properties of Stokes waves. In addition, the models are tested against experiments concerning periodic wave transformation over a bar topography and of the shoaling of solitary waves on a beach.