Boundary Conditions for the Simulation of Wave Breaking

Abstract

In this paper we propose a new numerical model for the simulation of the wave breaking. The threedimensional equations of motion are expressed in integral contravariant form and are solved on a curvilinear boundary conforming grid that is able to represent the complex geometry of coastal regions. A time-dependent transformation of the vertical coordinate that is a function of the oscillation of the turbulent wave boundary layer is proposed. A new numerical scheme for the simulation of the resulting equations is proposed. New boundary conditions at the free surface and bottom for the equations of motion expressed in contravariant form are proposed. We present an analysis of the importance of the correct positioning, inside the oscillating turbulent boundary layer, of the centre of the calculation grid cell closest to the bottom, in order to correctly simulate the height of the breaking waves.