Numerical Models for Obliquely Incident Waves in Surf and Swash Zones

摘要

Time-dependent numerical models are developed to predict the temporal and cross-shore variations of the free surface elevation and the cross-shore and alongshore fluid velocities in the swash and surf zones under obliquely incident waves. The assumption of shallow water with small incident angles and slow alongshore variations are made to reduce computational efforts considerably and to eliminate difficulties associated with lateral boundary conditions. These assumptions enable the models to compute the cross-shore fluid motion separately from the alongshore motion. The numerical models allow gradual alongshore variations of the bathymetry and the incident regular or irregular waves specified at the seaward boundary. Two numerical models are developed in this study. The first model is a two-dimensional (2D) model that neglects the vertical variations of the cross-shore and alongshore velocities. As a result, this model neglects the dispersion due to the vertical variations of the horizontal velocities and predicts only the depth-averaged cross-shore and alongshore velocities. The second model is a quasi three-dimensional (3D) model that assumes a cubic profile for the horizontal velocities and includes the dispersion terms due to the vertical variations of the horizontal velocities. Two additional equations for cross-shore and alongshore momentum flux corrections are derived. These numerical models are compared with available laboratory and field data for planar beaches. To assess the importance of the dispersion terms, both models are compared with the same data. Both models are shown to be capable of predicting the cross-shore variations of wave height, setup and runup for regular waves and root-mean-square wave height for irregular waves. The dispersion effects on wave height and setup are shown to be minor.