Implementation of boundary conditions for locked waves

Abstract

This report refers to the work done at the Fluid Mechanics Section within the framework of the Netherlands Centre for Coastal Research (NCK). As shown by Reniers et al. (2000) there are strong indications that wave-group related phenomena are important in the development of rip channels. It is to be expected that edge waves caused by wave-group induced long waves can be of significant influence on the development of the bathymetry and shoreline. In the development of research models for morphodynamic evolution in the coastal zone the first step is an accurate description of the flow field. In this project use is made of the Delft3D-flow solver to model waves at the scale of wave groups in the coastal zone. The Delft3D model was originally developed to model tide induced flow in sea, coast and estuaries. In this project we use the version of the model which uses the depth averaged flow option. For the boundary conditions used in a model intended for time scales corresponding with tidal flow the demands are not very high. The waves modelled by such models are extremely long and the phase changes along the open boundaries of the model very small. The Delft3D program therefore had a simplified version of the Riemann boundary conditions, effectively using the assumption that outgoing waves at the boundary were travelling perpendicularly to the boundary. On a time and space scale of wave groups this assumption proves to be insufficient as shown in Petit et. al. (2000). A program not equipped with boundary conditions that allow both locked and free waves to enter the domain and free waves to leave the domain without significant (non-physical) reflections, cannot be used for modeling long waves in the coastal zone accurately. It was shown that the Riemann boundary conditions developed by Van Dongeren and Svendsen (1997) could very well offer a solution to this problem. Tests with a simplified model t.hen showed that. these boundary condit.ions indeed performed very well. In the simplified test model use was made of prescribed wave forces. These were not related to numerically determined carrier wave densities. In the Delft3D adaptions, t.he wave forces are determined as minus the divergence of t.he radiation-stress tensor. This involves numerical differentiation of (multiples of) the carrier-wave energy. One of the problems encountered in making the Delft3D program suit.able for the simulation of short wave induced flow proved the determination of the wave forces near weakly reflective boundaries. This report describes a number of one-dimensional test cases used to locate the problems of the numerical approach. For one problem, regarding the numerical determination of the wave forces near the boundary, a solution was found by using extrapolation and by using a different discretization for the transport of wave energy near the boundary.