Propagation and transformation of nonlinear shallow water waves in irregular basins

This paper describes the development of a Boussinesq three-equation model for simulating nonlinear-wave propagation in an arbitrary shallow-water basin. The Boussinesq equations in terms of depth-averaged horizontal velocities and free-surface elevation are solved numerically in a curvilinear coordinate system. An Euler's predictor-corrector finite-difference algorithm is applied for numerical computation. The effects of irregular boundary, non-uniform water depth and coastal structures inside a basin are all included in the model simulation. A second-order cnoidal wave solution is used as an incident wave condition. A set of open boundary conditions is also developed to effectively transmit waves out of the computational domain. The model is tested by simulating waves propagating past an uneven bottom with a convex ramp topography. The evolution of wave propagation, diffraction and reflection in a harbor with different layout of inner and outer breakwaters is also studied. The simulated wave heights are compared with laboratory measurements.